Residual charged particles from previous discharges or external sources can produce some localized plasma regions, so called plasma patches in a discharge gap. Such plasma patches can affect the propagation morphology of passing streamers. Here we investigate how positive streamers interact with the plasma patches using a 3D PIC/MCC model. Simulations are performed in air with two planar electrodes, considering either an electron-ion or a purely positive ion plasma patch. When a positive streamer propagates through the electron-ion plasma patch, it shows a lower field enhancement, a weaker growth of electron density and a slower propagation velocity. If the plasma density in the patch is sufficiently high, it can even stop the propagation of streamer, however, streamer can restart from the other end of the patch after a while. In addition, the electron-ion plasma patch can change streamer's direction by electrostatic attraction or repulsion. If the plasma patch consists of purely positive ions, it can also slow down the propagation of streamer and change its direction by repulsion. In case of sufficiently high ion density, streamer's direction and velocity are strongly disturbed, resulting in splitting around the tip of the patch, the number of splitting channels increases with background electric field.