Field Research doesn't reset at a set time. /research gives you three tasks, and a new set of three shows up 12 hours after you finish all of them. Finished tasks wait for the rest of the set, so clearing all three is how you get new ones.
Rerolls
Don't like a task? You get one reroll a day, counted 24 hours from the last one. A new set doesn't give you an extra reroll.
What it pays
Each task pays ₽, there's a bonus for clearing all three, and every third set you finish adds a pack of Poké Balls.
What about Special Research?
/specialresearch is different: a story chain you work through in order, stage by stage, with no timers at all. Each stage pays a small reward, and the last one ends with a mythical Pokémon.