If one one wants to conduct a systematic review in the field of psychology and specifically in cognitive functioning what will be the valid database, acceptable to reputed journal?
I suggest that you look at systematic reviews published in journals that you would like to address. The methodology followed in these reviews (e.g., valid databases) will give you a guideline to follow.
I do not have experience in systematic reviews in the field of psychology, but if I were you, in addition to searching PubMed, I would start a free trial of PsycInfo database: