We introduce Shur and projective Schur subgroup of the Brauer group of a cocommutative coalgebra by means of twisted cogroup coalgebras and we study their properties. In particular we show that these subgroups are always torsion (in contrast with the whole Brauer group). Moreover, when С is coreflexive and irreducible both subgroups coincide with the coradical ones. We illustrate the theory with several examples.