DayOfYear as per Indian fiscal year
The sequence number of a day in a year that begins on april 1 can be calculated this way:

SELECT 1+
       DATEDIFF(day,
           DATEFROMPARTS(
               DATEPART(year, DATEADD(month, -3, [Date])),
               4,
               1),
           [Date]) AS FYdayNumber
FROM tableWithDates;


In essence, we're subtracting three months from the current date, then using that year to create a start-of-year date (year, april, 1), then calculating the number of days between that start-of-year date and the current date. Finally, add 1 in order to make the sequence start at 1.

If you just want the first day of your fiscal year, you can use

SELECT DATEFROMPARTS(
           DATEPART(year, DATEADD(month, -3, [Date])),
           4,
           1) AS firstDayOfFY
FROM tableWithDates;


As @MarkSinkinson pointed out in another answer, avoid (user-defined) scalar functions for performance and parallelisation reasons.