User defined functions cannot be called on Linked Server.
To work around this problem, use the Openquery function instead of the four-part naming convention.
You need to create following function in your DB where Linked Server needs to call.
CREATE FUNCTION [dbo].Function_Name(@Parameter INT)
RETURNS VARCHAR(8000)
AS
BEGIN
DECLARE @word sysname
EXEC LinkedServer.DatabaseName.dbo.sp_executesql
N'SELECT DatabaseName.dbo.Function_Name(@Parameter)'
,N'@Parameter int'
,@Parameter=@word OUTPUT
RETURN @word
END
For more details, kindly visit the link below.
http://developersmania.blogspot.com/2012/11/call-user-defined-function-on-linked.html[
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I hope this helps you.