What does this symbol that looks like a stylized "P" mean in each of Hajime no Ippo's matches? What does the symbol resembling a stylized "P" in each of Hajime no Ippo's matches mean? Is it a Japanese symbol for cheering maybe?
The symbol that looks like "P" is actually "ア", a katakana for letter "A".

According to Jisho, "Aaa" could mean:


  Aah!; Ooh!; Oh No!; Oh Boy!; expression of despair, resignation, boredom, disgust, etc.​


though it could also mean yelling, shouting, cheering (depending on the situation).