We report the first results of a subsolar mass compact binary search using the data from the first part of the fourth observing run (O4a) of the Advanced LIGO detectors. Subsolar mass neutron stars and black holes are not expected to form via standard stellar evolution, and their observation would signify a new class of astrophysical objects or the discovery of a component of dark matter. Our search covers binaries with primary masses 0.1 to $2M_{\odot }$ and secondary masses 0.1 to $1M_{\odot }$. We explicitly incorporate tidal effects up to $7\times {10}^5$ for extremely low mass neutron stars. Due to the recent development of efficient ratio filter dechirping frameworks, this search consisting of 25 million templates is now computationally feasible. No statistically significant candidates are identified. We place a 90% confidence upper limit on the merger rate ${\mathcal{R}}_{90}$ for subsolar mass black holes to be $<2.5\times {10}^4{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$ for a chirp mass of $0.2M_{\odot }$. We place the first constraints for binary neutron stars with tidal deformabilities up to $\sim 7\times {10}^5$ and improve the merger rate estimate by a factor $\sim 3$ in comparison to previous O3 tidal searches for tidal deformabilities $<{10}^4$. The advanced sensitivity of the O4a run enables an improvement in the subsolar mass black hole merger rate limits by more than $2\times$ over the previous three observing runs (O1–O3) combined. We constrain the effective local dark matter fraction to be ${\tilde{f}}_{\mathrm{PBH}}<0.5\%$ for $M_{\mathrm{PBH}}=0.4M_{\odot }$, approximately 2 times lower than the previous O1–O3 constraints. Given our model assumptions, our local dark matter fraction constraints are 2–10 times lower than the OGLE microlensing survey for $M_{\mathrm{PBH}}\ge 0.25M_{\odot }$.

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