  The primary objective of this paper is to develop a well-behaved class of
Heintzmann IIa [{\em H. Heintzmann, Z. Physik 228, 489-493 (1969)}] solution in
the context of $f(R,\, T)$ gravity. In the $f(R, T)$ framework, the
gravitational action includes both the Ricci scalar ($R$) and the trace of the
energy-momentum tensor ($T$). We chose a particular $f(R,\,T)$ model s.t.
$f(R,\,T) = R+2 \chi T$, where $\chi$ is known as the coupling parameter. This
solution describes a novel isotropic compact fluid sphere with positively
finite central pressure and density in this extended theory of gravity. The
results obtained analytically are better described by graphical representations
of the physical parameters for various values of the coupling parameter $\chi$.
The solution for a specific compact object, Vela X-1, with radius $\mathfrak{R}
= 9.56_{-0.08}^{+0.08}$ km and mass $\mathcal{M} = 1.77 \pm
0.08~\mathcal{M}_{\odot}$ [{\em M. L. Rawls et al. ApJ, 730, 25 (2011)}], is
shown here. We analyze the fundamental physical attributes of the star, which
reveals the influence of the coupling parameter $\chi$ on the values of
substance parameters. This helps us to make a fruitful comparison of this
modified $f(R,\, T)$ gravity with the standard GR and notice that it holds good
for stable compact objects. In this framework, the star under our consideration
exhibits a stable structure consistent with the Heintzmann IIa {\em ansatz}.
From all of our obtained graphical and numerical results, we can ultimately
conclude that our reported model is physically admissible and satisfies all the
physical criteria for an acceptable model.
