A search is presented for fractionally charged particles with charges below (Formula presented), using their small energy loss in the tracking detector as a key variable to observe a signal. The analyzed dataset corresponds to an integrated luminosity of (Formula presented) of proton-proton collisions collected at (Formula presented) in 2016-2018 at the CERN LHC. This is the first search at the LHC for new particles with a charge between (Formula presented) and (Formula presented), including an extension of previous results at a charge of (Formula presented). Masses up to 640 GeV and charges as low as (Formula presented) are excluded at 95% confidence level. These are the most stringent limits to date for the considered Drell-Yan-like production mode.