Magnetic field (B-field) is one of the important constituents of the interstellar medium. By characterizing with direction and strength, B-field couples with gas and dust grains through ions and governs the formation of molecular clouds into filamentary morphologies and eventually regulates the formation of baby stars in the dense cores. Multi-wavelength polarization technique is a promising tool to probe the plane-of-the-sky component of B-field across various orders of magnitude in gas densities and spatial scales. The B-field, turbulence, gravity, and stellar feedback interact with each other and dictate the structures of the clouds and star formation efficiency. However, the interplay among these parameters remain poorly constrained. This is because of the fact that in comparison to other key agents it is hard to probe the B-field and hence to measure the field strength. Thanks to the recently available wide-field optical and near-infrared polarimeters as well as sensitive far-infrared and sub-millimeter polarimeters, through which it is now possible to overcome this problem. In a recent study, we have found that despite of having ordered B-field morphology (based on optical and near-infrared polarimery) and quiescent physical conditions at low-density, large-scale of B213/Taurus region, we evidenced a complex B-field morphology at ~0.01 to ~0.1 pc scales of B213 cores (Eswaraiah et al. 2021, ApJL, 912, 27). This study was conducted based on the observations acquired from JCMT SCUBA2-POL2 as a part of the BISTRO project. These results imply that the B-field may become complex in the dense cores due to gas inflows into the filament, even in the presence of a substantial magnetic flux. In another study, we have witnessed a compressed B-field draped around the dense, massive clumps of Sh 201 (Eswaraiah et al. 2020, ApJ, 897, 90). This we attribute to the feedback effect of the H II region on the surface of the massive clumps. We hypothesize that the interplay of the thermal pressure imparted by the H II region, the B-field morphology, and the various internal pressures of the clumps (such as magnetic, turbulent, and gas thermal pressures) has various implications on guiding the expanding ionization fronts to form bipolar bubbles, and shielding and stabilizing the clumps against HII region feedback. Finally, I will briefly discuss the results from other ongoing works and shed some light on future directions.