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BORROWINGS - Schedule of Short-Term Arrangements with the FHLBNY (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024
Schedule of Short-Term Arrangements with the FHLBNY [Abstract]
Balance at end of year
Weighted average balance during the year	976
Maximum month-end balance during the year	$ 34,200
Average interest rate during the year	4.55%

X

- References

No definition available.

+ Details

Name:	mgyr_FederalHomeLoanBankAdvancesShortTermBalance
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- References

No definition available.

+ Details

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

X

- Definition

The calculated average balance outstanding for the year for all Federal Home Loan Bank advances as of the Balance Sheet date.

+ References

Reference 1: 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)(3)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

+ Details

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

X

- Definition

The calculated weighted average interest rate for Federal Home Loan Bank advances for the period ended as of the Balance Sheet date.

+ References

Reference 1: 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)(3)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The maximum balance outstanding at any month end during the period as of the Balance Sheet date.

+ References

Reference 1: 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)(3)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

+ Details

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Balance Type:	credit
Period Type:	instant