Lattice QCD (LQCD) is a theoretical non-perturbative approach for studying QCD dynamics numerically from first principles. LQCD is widely used for hadron structure calculations and is becoming a reliable tool, striving to control various sources of systematic uncertainties. Parton distribution functions (PDFs) have a central role in understanding the hadron structure and have been calculated in lattice QCD mainly via their Mellin moments.

In this talk, I will present selected results using an alternative new method to access PDFs proposed by X. Ji in 2013. This is the so-called quasi-distribution method, which relies on matrix elements of fast-moving hadrons and non-local operators. These are matched to the light-cone PDFs using Large Momentum Effective Theory (LaMET). The main focus of the talk is to demonstrate a novel calculation of twist-3 gT PDF, explored in lattice QCD for the first time. I will also show results from the first calculation of the chiral-even unpolarized and helicity quark generalized parton distributions (GPDs), extracted from numerical simulations of lattice QCD. The calculation is performed on one ensemble of two degenerate light, a strange and a charm quark (Nf=2+1+1) of maximally twisted mass fermions with a clover term, reproducing a pion mass of 260 MeV.