Gaurav N. GadbailAvik DeP. K. Sahoo2024-10-172024-10-172023-12-0310.1140/epjc/s10052-023-12288-yhttps://dspace-cris.utar.edu.my/handle/123456789/2832Symmetric Teleparallel Gravity allows for the reformulation of gravity in the form of nonmetricity by vanishing the contorsion term in the generic affine connection. Our focus is on investigating a recently proposed extension of this theory in which the Lagrangian has the form f(Q, C) by incorporating the boundary term C. In this work, we first use a reconstruction approach in f(Q, C) gravity that might admit the Lambda CDM expansion history. Furthermore, we perform a novel approach for cosmological reconstruction of f(Q, C) gravity in terms of e-folding, and it shows how any FLRW cosmology can arise from a specific f(Q, C) gravity. A variety of instances are provided using this approach in which f(Q, C) gravity is reconstructed to yield the well-known cosmic evolution: Lambda CDM era, acceleration/deceleration era which is equivalent to the presence of phantom and non-phantom matter, late-time acceleration with the crossing of phantom-divide line and transient phantom era.journal-article