  We investigate crystal structure and magnetic properties including spin
relaxation and magnetocaloric effect in NASICON type NaFe$_2$PO$_4$(SO$_4$)$_2$
sample. The Rietveld refinement of x-ray and neutron diffraction patterns show
a rhombohedral crystal structure with the R$\bar{3}$c space group. The
core-level spectra confirm the desired oxidation state of constituent elements.
The {\it dc}--magnetic susceptibility ($\chi$) behavior in zero field-cooled
(ZFC) and field-cooled (FC) modes show the ordering temperature $\approx$50~K.
Interestingly, the analysis of temperature dependent neutron diffraction
patterns reveal an A-type antiferromagnetic (AFM) structure with the ordered
moment of 3.8 $\mu_{B}$/Fe$^{3+}$ at 5~K, and a magnetostriction below $T_{\rm
N}=$ 50~K. Further, the peak position in the {\it ac}--$\chi$ is found to be
invariant with the excitation frequency supporting the notion of dominating AFM
transition. Also, the unsaturated isothermal magnetization curve supports the
AFM ordering of the moments; however, the observed coercivity suggests the
presence of weak ferromagnetic (FM) correlations at 5~K. On the other hand, a
clear bifurcation between ZFC and FC curves of {\it dc}--$\chi$ and the
observed decrease in peak height of {\it ac}--$\chi$ with frequency suggest for
the complex magnetic interactions. The spin relaxation behavior in
thermo-remanent magnetization and aging measurements indicate the glassy states
at 5~K. Moreover, the Arrott plots and magnetocaloric analysis reveal the
AFM--FM interactions in the sample at lower temperatures.
