Are Field research Pokemon influenced by anything?

Question

In certain Field Research quests, the reward for completion is a mystery Pokémon encounter.

I have been doing the last stages of the Let's Go Meltan quest, and one is to catch an Aerodactyl; and where I live, we don't really qualify for any of the spawn locations. So outside of raids or potentially hatching one, (which I don't think counts anyway), they are incredibly rare for me to find.

However, I recently completed a Field research quest (I don't know which one) and was rewarded with an Aerodactyl! I have no idea if this is linked or not, as the last one I caught was nearly a year ago, and I only just started this stage of the Let's Go Meltan quest this week.

Answer 1

Field Research rewards are indeed not random! However, it doesn't have anything to do with which Special Research you have active - it's just very good luck that you got a quest that rewards an aerodactyl while that quest was open.

Field Research objectives rotate in and out based on a schedule set by Niantic, and each type of Pokemon-awarding research will give you a specific Pokemon (or one from a very small set of possible Pokemon).

You can see the list of currently-available Field Research and resulting rewards here. Or, if you're interested in historical field research, Bulbapedia keeps a record of all Field Research tasks that awarded Pokemon and the Pokemon those quests awarded, both currently available and rotated out.

Judging by the list of currently available Field Research, I'd guess you got your aerodactyl from a "win 5 raids" Field Research.