SQL Server 2019

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CREATE TABLE dbo.Quarters
(
  StartDate     date,
  QuarterNumber tinyint,
  FiscalYear    int,
  NextQuarterStartDate AS (DATEADD(MONTH, 3, StartDate))
);

INSERT dbo.Quarters(StartDate, QuarterNumber, FiscalYear)
  VALUES('20200201',1,2020),
        ('20200501',2,2020),
        ('20200801',3,2020),
        ('20201101',4,2020),
        ('20210201',1,2021),
        ('20210501',2,2021),
        ('20210801',3,2021),
        ('20211101',4,2021),
        ('20220201',1,2022),
        ('20220501',2,2022),
        ('20220801',3,2022),
        ('20221101',4,2022);
12 rows affected

DECLARE @date date = GETDATE();

SELECT * FROM dbo.Quarters 
  WHERE @date >= StartDate
  AND @date < NextQuarterStartDate;


StartDate
QuarterNumber
FiscalYear
NextQuarterStartDate


2022-11-01
4
2022
2023-02-01


DECLARE @date date = '20220105';

SELECT * FROM dbo.Quarters 
  WHERE @date >= StartDate
  AND @date < NextQuarterStartDate;


StartDate
QuarterNumber
FiscalYear
NextQuarterStartDate


2021-11-01
4
2021
2022-02-01