Seesaw mechanism is a popular approach to give a viable explanation to the source of non-zero neutrino mass and to the cause of matter dominance of the Universe - two of the most important open problems that could not be answered by the Standard Model (SM) of Particle Physics. A minimal extension of the SM is studied, incorporating type-I+II seesaw mechanism with only one right-handed neutrino as fermion singlet and one Higgs triplet scalar. Both of these heavy particles contribute to the generation of tiny neutrino mass, the contribution being proportional to the corresponding heavy particle masses. But the new source of CP asymmetry is coming solely from the decay of the right-handed neutrino by one-loop vertex correction involving the Higgs triplet scalar. The predictability of the model is further enhanced by introducing Fritzsch type 2-zero and 3-zero textures for the neutrino mass matrix and the non-diagonal charged lepton mass matrix, respectively. The parameter space study is executed following the latest neutrino oscillation parameter data and the phenomenological importance of this hybrid texture is analysed. Leptogenesis is successfully achieved in 2-flavoured regime within the temperature range T⊂[1010,1012] GeV.