Let \((M,\xi)\) be an oriented connected contact manifold of dimension \(3\). The contact structure \(\xi\) is called positive if \(\xi={\text{ ker}}\alpha\) for some smooth \(1\)-form \(\alpha\) satisfying \(\alpha\wedge d\alpha\). Every surface \(\Sigma\) in such a contact manifold \((M,\xi)\) has a singular foliation \(\Sigma_\xi\) given by integrating the singular line field \(T_x\Sigma\cap\xi_x\). A contact structure \(\xi\) is said to be overtwisted if there is an embedded disk \(D\) which is everywhere tangent to \(\xi\) along \(\partial D\). A contact structure is tight if it is not overtwisted. Y. Eliashberg [Invent. Math. 98, No.3, 623-637 (1989; Zbl 0684.57012)] gave a complete classification of overtwisted contact structures on \(3\)-manifolds in terms of homotopy theory. Loosely speaking, a contact structure on a \(3\)-manifold is symplectically semi-fillable if it is one component of the boundary of some symplectic \(4\)-manifold. For more details, see J. B. Etnyre’s paper [Topology Appl. 88, 3–25 (1998; Zbl 0930.53049)]. Gromov and Eliashberg showed that a symplectically semi-fillable contact structure on a \(3\)-manifold must be tight. See M. Gromov’s paper [Invent. Math. 82, 307–347 (1985; Zbl 0592.53025)] and Y. Eliashberg’s [Proc. Symp., Durham/UK 1989, Lond. Math. Soc. Lect. Note Ser. 151, 45–72 (1990; Zbl 0731.53036)]. Recently, the gluing techniques for tight contact structures were developed by Colin and Makar-Limanov, [cf. V. Colin, Ann. Inst. Fourier 51, 1419–1435 (2001; Zbl 1107.53058); V. Colin, Bull. Soc. Math. Fr. 127, No.1, 43-69 (1999); addendum ibid. 127, 623 (1999; Zbl 0930.53053)]. Using the gluing techniques strengthened by K. Honda in [Duke Math. J. 115, 435–478 (2002; Zbl 1026.53049)] rather than resorting to symplectic filling techniques it is shown in this paper that the Seifert fibered space \(M_1\) over \(S^2\) with Seifert invariants \((-\frac{1}{2}, \frac{1}{4}, \frac{1}{4})\) admits a tight contact structure that is not weakly symplectically semi-fillable. Moreover it is briefly shown that the Seifert fibered space \(M_2\) over \(S^2\) with Seifert invariants \((-\frac{2}{3}, \frac{1}{3}, \frac{1}{3})\) admits two nonisotopic tight contact structures that are not weakly symplectically semi-fillable. Finally four open questions are given at the end of this paper.