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Let $R$ be a finite commutative unitary ring. An idempotent in $R$ is anelement $e\in R$ with $e^2=e$. Let $\Psi$ be a subgroup of the group ${\rmAut}(R)$ of all automorphisms of $R$. The $\Psi-$weighted Erd\H{o}s-Burgessconstant ${\rm I}_{\Psi}(R)$ is defined as the smallest positive integer $\ell$such that every sequence over $R$ of length at least $\ell$ must contain anonempty subsequence $a_1,\ldots, a_{r}$ such that $\prod\limits_{i=1}^r\psi_i(a_i)$ is one idempotent of $R$ where $\psi_1,\ldots,\psi_r\in \Psi$. Inthis paper, for the finite quotient ring of a Dedekind domain $R$, a connectionis established between the $\Psi-$weighted-Erd\H{o}s-Burgess constant of $R$and the $\Psi-$weighted Davenport constant of its group of units by all theprime ideals of $R$.

Weighted Erd\H{o}s-Burgess and Davenport constant in commutative rings