The physical processes of stars are encoded in their periodic pulsations. Millions of variable stars will be observed by the upcoming Vera Rubin Observatory's Legacy Survey of Space and Time. Here, we present a convolutional autoencoder-based pipeline as an automatic approach to search for anomalous periodic variables within The Zwicky Transient Facility Catalog of Periodic Variable Stars (ZTF CPVS). We encode their light curves using a convolutional autoencoder, and we use an isolation forest to sort each periodic variable star by an anomaly score with the latent space. Our overall most anomalous events share some similarities: they are mostly highly variable and irregular evolved stars. An exploration of multiwavelength data suggests that they are most likely Red Giant or Asymptotic Giant Branch stars concentrated in the disk of the Milky Way. Furthermore, we use the learned latent feature for the classification of periodic variables through a hierarchical random forest. This novel semi-supervised approach allows astronomers to identify the most anomalous events within a given physical class, accelerating the potential for scientific discovery.