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Ferroelectric nanostructures have recently attracted considerable research interests for the discovery of novel topological dipole states. However, currently the preparation of high-quality nanodot arrays remains challenging, precluding the clear characterization of the dipole states in the nanodots. Combining pulsed laser deposition method with circular anodic aluminum oxide template, we reported an unexpected growth of high crystalline quality $\mathrm{PbZ}{\mathrm{r}}_{0.52}\mathrm{T}{\mathrm{i}}_{0.48}{\mathrm{O}}_{3}$ nanodot array in quadrilateral shape with size being \ensuremath{\sim}80 nm. Piezoresponse force microscopy measurement on various regions of the sample shows that the nanodots form rather diverse in-plane domain patterns, with the appearance of abundant topological domain defects including flux-closure vortices, center-divergent vortices, center-convergent vortices, and antivortices. A deterministic control of the domain structure of the nanodots via applying an electric field is further achieved. The nanodots were found to favor a center-divergent vortex pattern under negative tip bias, although the domain patterns of the nanodots at the as-grown state are different. Phase field simulations were performed to reproduce the experimental observation, and our results indicate that the screening condition of the nanodots is far from the ideal ones assumed in previous theoretical modellings. The nanodots are potentially useful in developing multi-state and reconfigurable electronic devices.