Correct usage of “concededly”
Solution 1:
According to dictionaries such as the Oxford English Dictionary and Burton's Legal Thesaurus (via TFD), "concededly" means "admittedly". And it makes no sense to say '“Yes” Jamie says admittedly.'
It is correct to say '“Yes” Jamie conceded.' This specific usage is listed in several dictionaries, such as here. (Some people, however, would probably disapprove of this usage for stylistic reasons.)