The specific heat of (Cd1-x-yZnyMnx)3As2 with low Mn concentration (x
less-than-or-equal-to 0.067) and for two Zn contents (y = 0.14 and y =
0.34) has been measured in the temperature range of 1.5-30 K. The mag
netic contribution to the total specific heat has been analysed within
our generalized pair approximation model which takes into account the
complicated tetragonal crystal structure of Cd1-x-yZnyMnx)3As2. Assum
ing that the total Mn-Mn interaction strength is a sum of superexchang
e and the Bloembergen-Rowland exchange, we have obtained a very good a
greement between our approach and experiment by using the analytical f
ormulae with only two adjustable parameters, i.e. the first nearest-ne
ighbour exchange constants for both mechanisms which appear to be stro
ngly dependent on Zn content.