>I need to obtain the proper syntax to do a query on a character field based on the last four characters. For example, the record could have this value in that field: ThisIsMyFileName.ext. Thus, I need to locate the .ext record.

Well, it will be

FieldName LIKE '%[.]ext'

This will be non-sargable, so if you can create a computed column for extension and index on it, the performance will be better.