Any kind of pokeball can catch Mersprit, but it is best to use a Pokemon with mean look if you have troubles with it running away.
jiroxy ball...
if you mean the map marker you can catch mesprit Pokemon of emotions with it hope this helps
You should save the game right before you battle it (so if you lose, you can turn off the power and try again), use a move that blocks Mesprit from running, and use weak moves until Mesprit seems like it has 1 HP left (or u could catch a sneasel and teach it false swipe), then use a Poke-ball that seems to be the best for it. (Note:If Mesprit keeps on breaking out of the Poke-ball, then use weaker ones to try and stall it, and then use a good one. Heal Balls are better than they look.)
Mesprit does flee from the battles normally at the beginning. But if you manage to inflict damage on it then when you see it again it will still have the damage to it. The best way I found to catch Mesprit is to get a level 30-40 Pokemon that knows Mean Look, I evolved my gastly as i found my captured Haunters didnt know Mean Look. Then give your Pokemon that knows mean look a quick claw. Track down Mesprit using the Poketech app (forgot what it is called, my apologies >.
you catch it with a poke ball
A Master Ball
master ball
with a poke ball
use a poke ball
by throwing it
To catch a pokemon, you require a Poke ball, which you can buy from a poke mart.
you have to follow her to catch her like with mesprit. just follow your poke etch