Flow generated via peristaltic waves in naturally occurring physical phenomenon inside human body. Its combination with electric and magnetic forces makes it even more versatile in biomedical engineering applications. The results presented in this article are useful in designing artificial tubes, lab-on-a-chip devices for cell manipulation, drug design, flow amalgamation, micro-scale pumps and micro-bots which can be externally controlled by electric and magnetic sensors. Motivated by the aforesaid facts the current investigation is based on the transportation of a couple stress bio-fluid by peristalsis through a convergent channel under the postulates of creeping phenomena and long wavelength, respectively METHODS: A closed form solution is acquired for the axial velocity profile, volumetric flow rate and streamlines, respectively. The physical influence of involved parameters on the rheological characteristics are argued analytically with the help of Mathematica software 12.0.1 in detail. Additionally, the flow system is considered to take place under the both porosity and electro-magneto-hydrodynamics effects, respectively. The amplitude of axial velocity across one wavelength is strongly affected at the larger values of numerous embedded parameters: Darcy number, Hartmann number, Electro-osmotic velocity parameter and non-Newtonian (couple stress) parameter.We have observed remarkable effects of embedded parameters on velocity distribution, flow rate and trapping phenomena under porous and electro-osmotic (combination of both magnetic and electric) effects. The circulation of boluses and number of streamlines are reduced/enhanced for larger Hartmann number/Darcy number due strong magnetic/porosity effects. This research study additionally tells us how to control the transportation phenomena of biological fluids by appropriate adjusting the porosity effects (the effects of porous media) and electro-osmotic influences. Moreover, in order to enhance the performance of a peristaltic pump at the micro-scale level, we have used complex peristaltic wave scenario in the boundary walls of the convergent micro-channel.