Universal modified function in conjunction with the short range correlation effect to extract the nuclear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>x</mml:mi> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mn>3</mml:mn

Parton distribution functions (PDFs) are comprehensive and not reliant on the process. They are affected by nuclear matter during nuclear scattering process. As a recent approach, in order to study the nuclear PDFs (nPDFs), the nucleon pair PDFs are utilized to describe parton distributions in the nucleon pair which are confined to a nucleus. Nucleon pair PDFs stem from nucleon-nucleon correlation, which is called short range correlation (SRC) and are proportional to common nucleon PDFs. In this regard a modified universal function is constructed, which provides a test for SRC in (neutrino)-nucleus scattering. In fact we can show that the modification of the structure function of nucleons bound in atomic nuclei [known as the European Muon Collaboration (EMC effect)] are consistently accounted for within the framework of a universal modification of nucleons in SRC pairs. In this article, based on the strategy that was introduced in Schmookler et al. [Nature (London) 566, 354 (2019).], we are investigating to find the universality behavior for the ratio of nonsinglet $x{F}_{3}^{A}$ nuclear structure function. The numerical calculations performed within the CTEQ framework confirm the universality feature of the concerned ratio, as has been established for the ratio of the structure function ${F}_{2}^{A}$ in Schmookler et al. [Nature (London) 566, 354 (2019).]. Following that we reformulate the ${R}_{\mathrm{EMC}}$ nuclear weight function, which relates the free and bound structure function in terms of modified universal function. It makes us a possibility to achieve ${R}_{\mathrm{EMC}}$ and finally $x{F}_{3}^{A}$ nuclear structure function for each nucleus only by considering the specified feature of nucleus. The results are compared with the nuclear $x{F}_{3}$ structure function, which are computing from bound PDFs, based on some parametrization models. The findings, considering the SRC effect, demonstrate qualitative agreement with nCTEQ15 and EPPS21 parametrization models and also the available experimental data.