FSB Bancorp, Inc. (Parent Company Only) (Schedule of Statements of Income) (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018
Consolidated Statements of Income
Interest Income	$ 12,248	$ 11,827
Net (Loss) Income	(513)	135
Parent Company [Member] | Reportable Legal Entities [Member]
Consolidated Statements of Income
Interest Income	39	36
Other Expense	(447)	(500)
Equity in undistributed (loss) earnings of banking subsidiary	(105)	599
Net (Loss) Income	$ (513)	$ 135