  We derive an $\alpha=1/3$ - attractor potential of slow-roll inflation in the
geometric set-up of three intersecting $D7$ branes under $T^6/Z_N$ type of
$CY_3$-compactification within type IIB/F theory with some near-conifold
regions. The underlying quadratic structure of the kinetic poles is found to
arise from a correction in the K\"{a}hler potential when an extra contribution
of open string moduli is turned on. While the closed string sector of the
moduli spectrum is completely stabilized via quantum corrections of
perturbative and non-perturbative origin, the open string sector plays the lead
role in driving the inflationary expansion in the radial direction. A generic
asymptotic behavior of the inflaton field near the pole boundaries manifests as
the slow-roll plateau in canonical field space, which becomes responsible for
giving universal predictions of the cosmological parameters. We find that the
presence of the open strings near conifold regions brings the realization of
pole inflation in the present set up. Finally we compare our results with
similar models and discuss the importance of exploring precise values of
$\alpha$ in the light of ongoing and forthcoming cosmological surveys.
