I was playing a game today at a card shop against an employ that said if
I can beat him hell give me a free card of my choice. They had just
unveiled gym leaders and i got my booster packs(2). In one of them I
received Erika's Exeggute, who is a plant pokemon but has the move
Psychic. I used this move against his Alakazam but i was not sure whether
to do psychic or plant damage. which should i do?

The damage done with a Pokemon is the color of the Pokemon, not the color of the attack, thus Exeggecute's attack is Grass, not Psychic.