The ($^{16}\mathrm{O}$, $^{12}\mathrm{C}$) $\ensuremath{\alpha}$-transfer reaction has been studied on several Ca and Ti target isotopes using the 40- and 48-MeV $^{16}\mathrm{O}$ beams of the Saclay FN tandem Van de Graaff. This work is the natural extension of the previous one performed on various Fe and Ni target isotopes. As previously observed for Ni and Zn residual nuclei, a small number of levels are strongly and selectively excited at low energy. This $\ensuremath{\alpha}$-transfer reaction appears, then, as a new spectroscopic tool to study four-nucleon correlations. In close connection with the previous data on Fe and Ni targets, the present article points out the importance in residual nuclei of the quartet structure: namely two protons and two neutrons mutually strongly bound and weakly coupled to the target core. A strong blocking effect on the quartet is observed as soon as a neutron-pair excess is present in the target ground state. This neutron blocking effect has been already observed in the Fe and Ni target case. The existence in the $1f\ensuremath{-}2p$ shell of quartetting phenomena, i.e., the presence of four highly correlated nucleons giving rise to a quasirotational band, establishes the interplay between spherical and deformed states already known to exist in lighter nuclei.