We present results of three wide-band directed searches for continuous gravitational waves from 15 young supernova remnants in the first half of the third Advanced LIGO and Virgo observing run. We use three search pipelines with distinct signal models and methods of identifying noise artifacts. Without ephemerides of these sources, the searches are conducted over a frequency band spanning from 10 to 2 kHz. We find no evidence of continuous gravitational radiation from these sources. We set upper limits on the intrinsic signal strain at 95% confidence level in sample subbands, estimate the sensitivity in the full band, and derive the corresponding constraints on the fiducial neutron star ellipticity and r-mode amplitude. The best 95% confidence constraints placed on the signal strain are 7.7 × 10-26 and 7.8 × 10-26 near 200 Hz for the supernova remnants G39.2-0.3 and G65.7+1.2, respectively. The most stringent constraints on the ellipticity and r-mode amplitude reach ≲10-7 and ≲ 10-5, respectively, at frequencies above ∼400 Hz for the closest supernova remnant G266.2-1.2/Vela Jr.