We report here the controlled generation of polarization singularities (PS) in the output beam from a two-mode optical fiber, obtained via coherent superposition of the fundamental ( ${\mathrm{HE}}_{11}$ ) mode with the vortex ( ${\mathrm{CV}}_{\pm 1}^{\pm }/{\mathrm{IV}}_{\pm 1}^{\pm }$ ) modes by selectively coupling circularly polarized ( $\sigma =\pm 1$ ) Gaussian ( ${\mathrm{TEM}}_{00}$ ) input beam at two different launch angles. The PS in the output beam are characterized using the complex Stokes fields and interferometry measurements, based on the two-mode optical fiber which are an effective means to generate, manipulate, study, and use isolated PS, depending strongly on the input launch conditions.