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We study the impact of black hole nuclear activity on both the global and radial star formation rate (SFR) profiles in X-ray-selected active galactic nuclei (AGN) in the field of miniJPAS, the precursor of the much wider J-PAS project. Our sample includes 32 AGN with z < 0.3 detected via the XMM-Newton and Chandra surveys. For comparison, we assembled a control sample of 71 star-forming (SF) galaxies with similar magnitudes, sizes, and redshifts. To derive the global properties of both the AGN and the control SF sample, we used CIGALE to fit the spectral energy distributions derived from the 56 narrowband and 4 broadband filters from miniJPAS. We find that AGN tend to reside in more massive galaxies than their SF counterparts. After matching samples based on stellar mass and comparing their SFRs and specific SFRs (sSFRs), no significant differences appear. This suggests that the presence of AGN does not strongly influence overall star formation. However, when we used miniJPAS as an integral field unit (IFU) to dissect galaxies along their position angle, a different picture emerges. We find that AGN tend to be more centrally concentrated in mass with respect to SF galaxies. Moreover, we find a suppression of the sSFR up to 1Re and then an enhancement beyond 1Re, strongly contrasting with the decreasing radial profile of sSFRs in SF galaxies. This could point to an inside-out quenching of AGN host galaxies. Additionally, we examined how the radial profiles of the sSFRs in AGN and SF galaxies depend on galaxy morphology, by dividing our sample into disk-dominated (DD), pseudo-bulge (PB), and bulge-dominated (BD) systems. In DD systems, AGN exhibit a flat sSFR profile in the central regions and enhanced star formation beyond 1Re, contrasting with SF galaxies. In PB systems, SF galaxies show a decreasing sSFR profile, while AGN hosts exhibit an inside-out quenching scenario. In BD systems, both populations demonstrate consistent flat sSFR profiles. These findings suggest that the reason we do not see differences on a global scale is because star formation is suppressed in the central regions and enhanced in the outer regions of AGN host galaxies. While limited in terms of sample size, this work highlights the potential of the upcoming J-PAS as a wide-field low-resolution IFU for thousands of nearby galaxies and AGN. [ABSTRACT FROM AUTHOR]