There are Two approaches you could use to add the string and fret information. one is to use the sender() function to get the button which emitted the signal. you can the access fret and string if they are members of your button class so in the SLOT you would have.
MyPushButton *button = (MyPushButton *)sender();
button.getFret();
button.getString();
However since you are already subClassing QPushButton you could use a private SLOT to catch the buttonClicked signal and re-emit a signal with the right values.
In the constructor
connect(this, SIGNAL(clicked()), this, SLOT(reemitClicked()));
and then the reemit SLOT
void MyPushButton::reemitClicked()
{
emit clicked(m_fret, m_string);
}
be sure to add the appropriate private slot and public signal to you class
https://doc.qt.io/archives/qq/qq10-signalmapper.html see this artical for a good discussion on various ways to add an argument to signal.