How can I deal with mild paranoia and depression?

Medications. First of all, good diagnosis is needed. Is paranoia a part of depression or you have psychosis ( paranoia) and in this case people have symptoms that are resembling depression (so-called negative symptoms). The treatment is antidepressants in first case and antipsychotics in second case. Anyway, paranoia ( if you really mean what doctors mean when they say paranoia) needs careful investigation.