A proper patch requires materials specific to the material your liner is made out of. Each manufacturer defines these materials and the correct application method. They all require a clean dry liner.

Beyond that I've seen people post all kinds of goops to fix leaks underwater. From poly foam to epoxy to silicone to tar stuff. The list is pretty much anything. That's the internet.

For mud bottom ponds bentonite clay is sometimes used effectively to slow water loss. I wouldn't exactly say it makes a pond water tight, but often good enough. So I guess the clay could get behind the liner and seal the soil. Could cause your liner to float. I certainly wouldn't recommend it for a small backyard type pond. Just passing along the info.

So imo there isn't anything that would seal a liner hole that works underwater and is even somewhat reliable.

I don't know if this works, but it's supposed to work underwater.

Here is a link that might be useful: Underwater adhesive

Look at this page. Believe that You find the right information

Here is a link that might be useful: Underwater ship repair

I would get 2 pieces of 1/4" Plexiglas and bolt them together (w/ stainless steel bolts) and sandwich the hole (liner) between the Plexiglas.

I have no idea how big the hole is and the access you have to the hole.

Another option: If the hole is small say 1/4", push a 1/2 PVC pipe with a glue cap on it thru the hole, then pull the pipe back a little & clamp the liner to the PVC.

This is the best I can suggest with limited info on your situation.