The problem with
locate might be an outdated database. locate uses a database to show you result and that database is not updated real-time. So new files are not added to it when created. They will get added when the database is updated.
updates it for you manually but this is also done daily by cron on a default Ubuntu. locate is not real-time but very fast. locate accepts wildcards.
should give you results if the database is up to date and there are any files ending with ".t". You can filter the results by adding a
| grep Western (the example I show above would show 1 result; the last one would be shown) if you get too many results.
find is real-time and as a result it is slower than
find will show an error if you search location you are not allowed to search. The command in comments by @g_p is correct and searches from the current location files ending in ".t".
find . -type f -name "*.t"
which is not intended to find files but to find commands so is the wrong tool.
whereis is also not intended to find files but you can use to find the binary, source, and manual page files for a command.