  Let $F$ be a finite field of $char F > 3$ and $sl_{2}(F)$ be the Lie algebra
of traceless $2\times 2$ matrices over $F$. This paper aims for the following
goals:
  Find a basis for the $\mathbb{Z}_{2}$-graded identities of $sl_{2}(F)$;
  Find a basis for the $\mathbb{Z}_{3}$-graded identities of $sl_{2}(F)$ when
$F$ contains a primitive 3rd root of one;
  Find a basis for the $\mathbb{Z}_{2}\times \mathbb{Z}_{2}$-graded identities
of $sl_{2}(F)$.
