Base editors hold promise for correcting pathogenic mutations, while substantial single nucleotide variations (SNVs) on both DNA and RNA were generated by cytosine base editors (CBEs). Here we examined possibilities to reduce off-target effects by engineering cytosine deaminases. By screening 24 CBEs harboring various rAPOBEC1 (BE3) or human APOBEC3A (BE3-hA3A) mutations on the ssDNA or RNA binding domain, we found 8 CBE variations could maintain high on-target editing efficiency. Using Genome-wide Off-target analysis by Two-cell embryo Injection (GOTI) method and RNA sequencing analysis, we found DNA off-target SNVs induced by BE3 could be completely eliminated in BE3 R126E but the off-target RNA SNVs was only slightly reduced. By contrast, BE3-hA3A Y130F abolished the RNA off-target effects while could not reduce the DNA off-target effects. Notably, BE3 R132E , BE3 W90Y+R126E and BE3 W90F+R126E achieved the elimination of off-target SNVs on both DNA and RNA, suggesting the feasibility of engineering base editors for high fidelity deaminases.