my sympathies; that's too bad; my condolences
Polite expression used to show sympathy for someone's misfortune or loss. Often used as a set phrase.
My sympathies, that must have been tough.
I heard about your family. My condolences.
残念 expresses one's own regret or disappointment about a situation, while お気の毒に specifically conveys sympathy for someone else's misfortune.
気の毒 is the plain adjective describing something pitiable, while お気の毒に is its polite adverbial form used to directly express sympathy to someone.
Polite prefix お + 気の毒 (regrettable, pitiful) + adverbial particle に. The phrase literally means 'in a regrettable manner' and is used as a set expression of sympathy.