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We call a projective surface $X$ mixed quasi-\'etale quotient if there existsa curve $C$ of genus $g(C)\geq 2$ and a finite group $G$ that acts on $C\timesC$ exchanging the factors such that $X=(C\times C)/G$ and the map $C\times C\rightarrow X$ has finite branch locus. The minimal resolution of itssingularities is called mixed quasi-\'etale surface. We study the mixedquasi-\'etale surfaces under the assumption that $(C\times C)/G^0$ has onlynodes as singularities, where $G^0\triangleleft G$ is the index two subgroup ofthe elements that do not exchange the factors. We classify the minimal regularsurfaces with $p_g=0$ whose canonical model is a mixed quasi-\'etale quotientas above. All these surfaces are of general type and as an important byproduct,we provide an example of a numerical Campedelli surface with topologicalfundamental group $\bbZ_4$, and we realize 2 new topological types of surfacesof general type. Three of the families we construct are $\bbQ$-homologyprojective planes.

Mixed quasi-\'etale surfaces, new surfaces of general type with $p_g=0$ and their fundamental group