StepMonitor just returns p1
and that's it.
fitm = FindFit[
datint, {k1*int[q, {p1, p2, p3, p4}, h, \[Sigma]] + c}, {{\[Sigma],
0.0086}, {p1, -0.487}, {p2, 1.07}, {p3,
0.211}, {p4, -0.1264}, {k1, (2*10^6)^-1}, {h, 17}, {c, 0.001}},
q , Method -> "LevenbergMarquardt", StepMonitor -> Print[p1]]