Hey, I was wondering if there are any exercises that would help with this.

Basically a lot of songs I'm learning, the thumb plucks the bass notes at a constant rhythm while the other fingers pluck.

The trouble is that I find it hard to keep my thumb on beat while my index and middle finger do the other plucking.

Whats the best way to practice this?
The only thing I can really say about it is to make sure you start off with something simple and gradually make it more complicated as it gets easier for you; diving in at the deep end is only going to confuse and frustrate you.
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Try practicing just the thumb beat. When that's perfectly on rhythm, try plucking the high notes together. Then eventually you can divide the high notes into the actual rhythm.
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Start with something simple. A lot of iron and wine stuff has a constant thumb beat alternating with picking with other fingers. After that, find stuff that has patterns. Sort out the pattern and play it very slowly. Big love by fleetwood mac is one that helped me learn this. It has several different patterns and they aren't incredibly complex since the upper strings hit either between the thumb notes or at the same time as the bass notes.

After you can do a couple different patterns, you should be able to play a lot of other folk or blues stuff. They are normally fairly simple as long as you make sure you learn them slowly and with the correct timing.

Just make sure you keep working on different patterns of fingerpicking so that you can keep learning and improving your rhythm and finger control and you'll be able to get it eventually.

Do something like that in simple 4/4. Metallica's "Nothing Else Matters" should be good practice.