、。
Yoshio kept on believing it, despite counter-evidence.
Literal
Yoshio [topic-は] counter-evidence [subject-が] exists-[despite-にもかかわらず], so believing-continued
~にもかかわらず ('despite X, in spite of X') is a formal concessive marker, attached after a full clause or noun. More literary than でも or のに. 信じ続ける is a compound: 信じる (to believe) + 続ける (to continue) = to keep on believing. The そう ('so', 'in that way') refers to something previously stated.