We model the impact of non-uniform cloud cover on transit transmission spectra. Patchy clouds exist in nearly every solar system atmosphere, brown dwarfs, and transiting exoplanets. Our major findings suggest that fractional cloud coverage can exactly mimic high mean molecular weight atmospheres and vice-versa over certain wavelength regions, in particular, over the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) bandpass (1.1-1.7 \(\mu\)m). We also find that patchy cloud coverage exhibits a signature that is different from uniform global clouds. Furthermore, we explain analytically why the "patchy cloud-high mean molecular weight" degeneracy exists. We also explore the degeneracy of non-uniform cloud coverage in atmospheric retrievals on both synthetic and real planets. We find from retrievals on a synthetic solar composition hot Jupiter with patchy clouds and a cloud free high mean molecular weight warm Neptune, that both cloud free high mean molecular weight atmospheres and partially cloudy atmospheres can explain the data equally well. Another key find is that the HST WFC3 transit transmission spectra of two well observed objects, the hot Jupiter HD189733b and the warm Neptune HAT-P-11b, can be explained well by solar composition atmospheres with patchy clouds without the need to invoke high mean molecular weight or global clouds. The degeneracy between high molecular weight and solar composition partially cloudy atmospheres can be broken by observing the molecular Rayleigh scattering differences between the two. Furthermore, the signature of partially cloudy limbs also appears as a \(\sim\)100 ppm residual in the ingress and egress of the transit light curves, provided the transit timing is known to seconds.