Bitcoin mining endgame question

So 21 million Bitcoin is the limit that's going to be mined.

I've read that it will never technically hit that, just exponentially smaller amounts will be mined.

In either event, what will happen to verification, since mining is what verifies the ledger?

Is the return on mining going to be exponential with the work required to complete a block, what does incentive look like to keep verifying if the returns end? Or is there something else I'm missing?