Low-temperature specific heat (SH) is measured for the 12442-type KCa$_2$Fe$_4$As$_4$F$_2$ single crystal under different magnetic fields. A clear SH jump with the height of $Delta C/T|_{T_c}$ = 130 mJ/mol K$^2$ is observed at the superconducting transition temperature $T_c$. It is found that the electronic SH coefficient $Deltagamma (H)$ quickly increases when the field is in the low-field region below 3 T and then considerably slows down the increase with a further increase in the field, which indicates a rather strong anisotropy or multi-gap feature with a small minimum in the superconducting gap(s). The temperature-dependent SH data indicates the presence of the $T^2$ term, which supplies further information and supports the picture with a line-nodal gap structure. Moreover, the onset point of the SH transition remains almost unchanged under the field as high as 9 T, which is similar to that observed in cuprates, and placed this system in the middle between the BCS limit and the Bose-Einstein condensation.
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