Neither is quite a standard romanization but romanization of cyrillic tends to be up to the preference of the person more often than not (my own real name is not romanized in the standard way because the standard would be too confusing for english speakers)
Алексей Пажитнов in standard romanization would be Aleksei Pazhitnov, so I’m sure he went with Alexey Pajitnov when he immigrated to the US simply because english speakers are more likely to get the pronunciation close enough with that spelling.
the zh/j is the same sound as the ‘g’ in genre’