[sql-server] How to set value to variable using 'execute' in t-sql?

The dynamic SQL is a different scope to the outer, calling SQL: so @siteid is not recognised

You'll have to use a temp table/table variable outside of the dynamic SQL:

DECLARE @dbName nvarchar(128) = 'myDb'
DECLARE @siteId TABLE (siteid int)

INSERT @siteId
exec ('SELECT TOP 1 Id FROM ' + @dbName + '..myTbl')  

select * FROM @siteId

Note: TOP without an ORDER BY is meaningless. There is no natural, implied or intrinsic ordering to a table. Any order is only guaranteed by the outermost ORDER BY