As mentioned already, you need a calendar. You can generate one dynamically but far better to create a static one since it serves so many useful purposes. This is but one of many discussions about how to generate one.
A calendar is just a special form of a tally table and I use Itzik's discussion as a basis for that. Both of these concepts are things you need to understand in most SQL query writing environments.
Once you have a calendar, you simply join your data table to the calendar and filter as needed. I did not understand exactly what you were trying to accomplish so I simply create the set of rows for "Tuesday".
declare @EmpDetails1 table (id int, name varchar(20), startdate date, enddate date);
insert @EmpDetails1 (id, name, startdate, enddate) values
(1, 'Test 1', '20210101', '20210110'),
(2, 'Test 2', '20210116', '20210126');
select emp.*, cal.*, datename(weekday, cal.caldt) as [day of week(eng)]
from @EmpDetails1 as emp
inner join calendar as cal
on cal.caldt between emp.startdate and emp.enddate
and datename(weekday, cal.caldt) = 'Tuesday'
order by emp.id, cal.caldt
;
Fiddle here to demonstrate. I must highlight the lazy usage of * as the column list but this is just a simple demo. Production code should generally always specify the columns needed completely.
If you examine the calendar table discussion, you will see that the day of week can be easily added to the table - it will never change. This will avoid the effort to calculate it in the query.