Actually you have to keep value as NULL and check in your front end if the value is NULL don't show anything.
If for some reason you don't want to allow NULL in the column, it will save 01-01-1900 and then you check in your front-end if the value is 01-01-1900, don't show value.
Alternatively, in your stored procedure you can set like
select column1, column2,
case when convert(varchar(10),yourDatecolumn,101) = '01-01-1900'
else yourDateColumn end) as modifiedDate
I don;t have SQL access now, so correct the sytax before using.
Hoep that helps. If it does, mark it as answer/upvote.