We have extracted 636 spectra taken at the positions of 583 transient sources from the third data release of the Hobby-Eberly Telescope Dark Energy eXperiment (HETDEX). The transients were discovered by the Zwicky Transient Facility (ZTF) during 2018-2022. The HETDEX spectra provide a potential means to obtain classifications for a large number of objects found by photometric surveys for free. We attempt to explore and classify the spectra by utilizing several template-matching techniques. We have identified two transient sources, ZTF20aatpoos = AT 2020fiz and ZTF19abdkelq, as supernova (SN) candidates. We classify AT 2020fiz as a Type IIP SN observed ~10d after explosion, and we propose ZTF19abdkelq as a likely Type Ia SN caught ~40d after maximum light. ZTF photometry of these two sources are consistent with their classifications as SNe. Beside these two objects, we have confirmed several ZTF transients as variable active galactic nuclei based on their spectral appearance, and determined the host galaxy types of several other ZTF transients.