Permutation polynomials hold significant relevance in the practical applications of finite fields. Presently, they constitute a pivotal focus in contemporary research endeavors. This paper undertakes the classification of permutation binomials and trinomials of the form x(xs1 (q+1)+bs2 (q+1)+a) over Fq2, with s1=3. We explore these polynomials with variations in b, considering the cases where b = 0 or b ≠ 0 with s2 =1 and s2 = 2.