  We study the Ext modules in the category of left modules over a twisted
algebra of a finite quiver over a ringed space $(X,\mathcal O_X)$, allowing for
the presence of relations. We introduce a spectral sequence which relates the
Ext modules in that category with the Ext modules in the category of $\mathcal
O_X$-modules. Contrary to what happens in the absence of relations, this
spectral sequence in general does not degenerate at the second page. We also
consider local Ext sheaves. Under suitable hypotheses, the Ext modules are
represented as hypercohomology groups
