How to pass in a string into dynamic sql inside a stored procedure

Learn to use parameters with sp_executesql. You can do this for @searchtrtype, but not @orderbycondition:

SET @query =  N'
SELECT y.ID, y.STATUS,y.CONTROLID,y.TRCDE
FROM YTDTRNI y LEFT JOIN
     VND v
     ON y.COMNO = v.COMNO 
WHERE TRCDE = @searchtrtype 
ORDER BY @orderbycondition';

SET @query = REPLACE(@query, '@orderbycondition', @orderbycondition);

EXEC sp_executesql @query,
                   N'@searchtrtype NVARCHAR(255)',   -- or whatever the right type is
                   @searchtrtype=@searchtrtype;

You cannot pass in identifiers, only values, so this doesn't work for @orderbycondition.

You need to parametrise your SQL. Concatenating string for SQL is an awful idea; as it leaves you open to injection. The way you want to do it would be:

DECLARE @query nvarchar(MAX);
SET @query =  N'SELECT y.ID,' + NCHAR(10) + 
              N'       y.STATUS,' + NCHAR(10) + 
              N'       y.CONTROLID,' + NCHAR(10) + 
              N'       y.TRCDE' + NCHAR(10) + 
              N'FROM YTDTRNI AS y' + NCHAR(10) + 
              N'     LEFT JOIN VND AS v ON y.COMNO = v.COMNO ' + NCHAR(10) + 
              N'WHERE TRCDE = @dsearchtrtype' + NCHAR(10) + 
              N'ORDER BY ' + QUOTENAME(@orderbycondition) + N';';
PRINT @SQL;

EXEC sp_executesql @query, N'@dsearchtrtype nvarchar(100)', @dsearchtrtype = @searchtrtype;

This, however, probably isn't going to work, due to your variable @orderbycondition. I don't know, however, what type of value that has, however, if it's something like 'ID desc', this it would become ORDER BY [ID desc];.

If this assumption is correct, I would suggest using 2 variables; one for the sort column and one for the direction, and replace the final line of the dynamic SQl with:

N'ORDER BY ' + QUOTENAME(@orderbycolumn) + N' ' + CASE WHEN @orderbydirection NOT IN(N'ASC',N'DESC') THEN N'' ELSE @orderbydirection END + N';';

If your value of @orderbycondition can be more complex than that, post a comment to let me know (and update your question with more detail), and I'll be happy to explain how to create a more dynamic ORDER BY clause using a table type parameter, along with adding it to your dynamic SQL with use of STUFF and FOR XML PATH.

Based on the example provided it appears that the OP simply wants to filter on a single column and perform a sort on a user specified column. This can be achieved with a parametrized query without the need of dynamic SQL.

Within the where clause the TRCDE field can be directly assigned to the @searchtrtype parameter. The dynamic sorting requirement is a little trickier but can be achieved by using a CASE statement within the ORDER BY clause. An additional parameter will have to be included to indicate if the sorting should be ascending or descending. The following query demonstrates:

DECLARE @orderByColumn  NVARCHAR(50) = 'ID'; -- The column to sort by
DECLARE @sortAscending BIT = 1; -- Indicate sorting order 1 == Ascending, 0 == Descending
DECLARE @searchtrtype NVARCHAR(10) = 'RC'

IF @sortAscending = 1 -- Sort data in ascending order
BEGIN

    SELECT       y.[ID]
                ,y.[STATUS]
                ,y.[CONTROLID]
                ,y.[TRCDE]
    FROM        YTDTRNI AS y 
    LEFT JOIN   VND AS v ON y.[COMNO] = v.[COMNO]
    WHERE       TRCDE = @searchtrtype 
    ORDER BY    (
                    -- Create case statement for every column user may want to filter on
                    CASE
                        WHEN @orderByColumn = 'ID' THEN [ID]
                        ELSE NULL -- Simply return null if we are not ordering by this column, effectively ignore the column.
                    END
                 ),
                 (
                    CASE
                        WHEN @orderByColumn = 'STATUS' THEN [STATUS]
                        ELSE NULL -- Simply return null if we are not ordering by this column, effectively ignore the column.
                    END
                 ),
                             (
                    CASE
                        WHEN @orderByColumn = 'CONTROLID' THEN [CONTROLID]
                        ELSE NULL -- Simply return null if we are not ordering by this column, effectively ignore the column.
                    END
                 ) ASC;
END
ELSE
BEGIN
    SELECT       y.[ID]
                ,y.[STATUS]
                ,y.[CONTROLID]
                ,y.[TRCDE]
    FROM        YTDTRNI AS y 
    LEFT JOIN   VND AS v ON y.[COMNO] = v.[COMNO]
    WHERE       TRCDE = @searchtrtype 
    ORDER BY    (
                    CASE
                        WHEN @orderByColumn = 'ID' THEN [ID]
                        ELSE NULL -- Simply return null if we are not ordering by this column, effectively ignore the column.
                    END
                 ),
                 (
                    CASE
                        WHEN @orderByColumn = 'STATUS' THEN [STATUS]
                        ELSE NULL -- Simply return null if we are not ordering by this column, effectively ignore the column.
                    END
                 ),
                             (
                    CASE
                        WHEN @orderByColumn = 'CONTROLID' THEN [CONTROLID]
                        ELSE NULL -- Simply return null if we are not ordering by this column, effectively ignore the column.
                    END
                 ) DESC;
END

This method is more work but will be easier to troubleshoot, maintain and will protect you from SQL Injection.

do you just need to include escaped apostrophes. if @searchtrtype can contain apostrophes, you might have to escape them with REPLACE(@searchtrtype, '''', '''''')

SET @query =  N'SELECT y.ID, y.STATUS,y.CONTROLID,y.TRCDE
FROM YTDTRNI AS y LEFT JOIN VND AS v ON y.COMNO = v.COMNO 
WHERE TRCDE = ''' + @searchtrtype + ''' 
ORDER BY ' + @orderbycondition