I'm trying to find the correct lens mount or adapter to use with my Canon T3i. The mount has patent number 3500735 and says "For Canon".
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The "For Canon" is a pretty big hint, narrowing things down significantly. Since it's clearly not the current "EOS" mount, the obvious guess is that it's the previous manual-focus Canon mount, called "FD".
You can find adapters fairly easily (like this one), but note that because the flange focal distance of the older mount is shorter, the adapter needs to contain glass in order to retain focus at a distance, which means that (especially with a $40 adapter) image quality will be compromised. (So, basically, unless you're just doing it for fun, it's not necessarily worth it.)
However, the patent number 3500735 and exposed gear on the side indicates that the mount shown is not on the lens itself, but on an adapter for a Tamron universal mount. I would need more pictures to see which adapter it is, but I would guess it is for the Adaptall-2 bayonet mount. If that is the case, you can get an Adaptall-EF (Tamron-EOS) adapter to use the lens with your Canon camera. To detach the existing adapter from the lens, you need to press a tab on the side to release it.
Mounts that can be adapted to EF/EF-S include: