Let \(X,Y\) be Banach spaces, \(C\) be a cone in \(X\) and let \(\Omega_1,\Omega_2\) be open bounded subsets of \(X\) with \(\overline{\Omega}_1\subset\Omega_2\). For a pair \((L,N)\) consisting of a linear Fredholm operator \(L:\text{dom}\,L\subset X\to Y\) of zero index and an upper semicontinuous (compact convex)-valued multimap \(N:X\multimap Y\), the authors study the existence of a coincidence point \((Lx \in Nx)\) in \(C\cap(\overline{\Omega}_2\setminus\Omega_1)\). They use topological degree methods under some compactness or condensivity conditions. As application, the existence of positive periodic solutions for a differential inclusion is considered.