We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters spanning $0.4-0.9\mu\mathrm{m}$) and novel JWST images with 14 filters spanning $0.8-5\mu\mathrm{m}$, including 7 medium-band filters, and reaching total exposure times of up to 46 hours per filter. We combine all the imaging data at $>2\mu\mathrm{m}$ to construct the deepest imaging ever taken at these wavelengths, reaching as deep as $\approx31.4$ AB mag in the stack and 30.1-30.8 AB mag ($5\sigma$, $r=0.1"$ circular aperture) in individual filters. We measure photometric redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts $z=11.5-15$. These objects show compact half-light radii of $R_{1/2}\sim50-200$pc, stellar masses of $M_\star\sim10^7-10^8M_\odot$, and star-formation rates of $\mathrm{SFR}\sim0.1-1~M_\odot~\mathrm{yr}^{-1}$. Our search finds no candidates at $15Comment: 33 pages, 21 figures. Submitted to AAS Journals