Let M be the 3-manifold obtained by r-surgery on the right handed trefoil knot. Classification of contact structures on such manifolds have been mostly understood for r\geq 1 and r=0. Etnyre-Min-Tosun has an upcoming work on the classification of the tight contact structures for all r. The fillability of contact structures on M is mostly understood if r is not between 0 and 1/2.  In this talk, we will discuss the fillability of the contact structures M for 0<r<1/2. How many contact structures does M admit? How many of them are strongly fillable but not Stein fillable? This is a joint work with Prof. John Etnyre.