LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Details) - Schedule of Loans Receivable, Net - USD ($) $ in Thousands	9 Months Ended	12 Months Ended
Jun. 30, 2023	Sep. 30, 2022
Schedule of Loans Receivable, Net [Abstract]
Total loans receivable	$ 702,530	$ 628,904
Net deferred loan fees	(844)	(628)
Allowance for loan losses	(8,378)	(8,433)
Total loans receivable, net	693,308	619,843
One-to-four family residential [Member]
Schedule of Loans Receivable, Net [Abstract]
One-to-four family residential	236,633	214,377
Total loans receivable	236,633	214,377
Commercial real estate [Member]
Schedule of Loans Receivable, Net [Abstract]
Commercial real estate	402,349	342,791
Total loans receivable	402,349	342,791
Construction [Member]
Schedule of Loans Receivable, Net [Abstract]
Construction	19,249	15,230
Total loans receivable	19,249	15,230
Home equity lines of credit [Member]
Schedule of Loans Receivable, Net [Abstract]
Home equity lines of credit	18,737	18,704
Total loans receivable	18,737	18,704
Commercial business [Member]
Schedule of Loans Receivable, Net [Abstract]
Commercial business	23,129	34,672
Total loans receivable	23,129	34,672
Other [Member]
Schedule of Loans Receivable, Net [Abstract]
Other	2,433	3,130
Total loans receivable	$ 2,433	$ 3,130

Amount of commercial business.

No definition available.

Name:	mgyr_CommercialBusiness
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of home equity lines of credit.

+ References

No definition available.

+ Details

Name:	mgyr_HomeEquityLinesOfCredit
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of deferred costs incurred to originate loans and leases from face amounts of acquired loans.

+ References

No definition available.

+ Details

Name:	mgyr_LoansAndLeasesReceivableDeferredCost
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of family residential.

+ References

No definition available.

+ Details

Name:	mgyr_OnetoFourfamilyResidential
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_AccountsNotesAndLoansReceivableLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of other addition (reduction) in allowance reserve for credit loss.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 15
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481962/310-10-50-15

+ Details

Name:	us-gaap_AllowanceForLoanAndLeaseLossesAdjustmentsNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Carrying value as of the balance sheet date of short-term borrowings using unsecured obligations issued by banks, corporations and other borrowers to investors. The maturities of these money market securities generally do not exceed 270 days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(1))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479440/944-210-S99-1

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479853/942-210-S99-1

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19)(a)(3))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_CommercialPaper
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of structure or a modification to a structure under construction. Includes recently completed structures or modifications to structures that have not been placed into service.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 360
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482099/360-10-50-1

+ Details

Name:	us-gaap_ConstructionInProgressGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of deferred interest and fee income, unamortized costs incurred to originate loans and leases, unamortized loan commitments and loan syndication fees, and premiums over or discounts from face amounts of acquired loans. Excludes amounts for loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 310
-SubTopic 20
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481569/310-20-50-3

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 840
-SubTopic 30
-Section 50
-Paragraph 4
-Subparagraph (a)(4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481161/840-30-50-4

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481962/310-10-50-4

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.7)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479853/942-210-S99-1

+ Details

Name:	us-gaap_LoansAndLeasesReceivableDeferredIncome
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount before allowance of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Includes deferred interest and fees, undisbursed portion of loan balance, unamortized costs and premiums and discounts from face amounts. Excludes loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481990/310-10-45-2

+ Details

Name:	us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount due from parties in nontrade transactions, classified as other.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(5)(a)(5))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479617/946-210-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(3)(a)(4))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_OtherReceivables
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_Residential1To4FamilyRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_ConstructionLoansMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_HomeEquityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_FinancingReceivableOtherMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: