Depends on your existing GraphicItems (I guess they have a custom type, no standard Qt-class objects?)

Something like this might work for you:

void MyPolygonShape::mousePressEvent(QGraphicsSceneMouseEvent *event)
{
    qDebug() << "Hello, it's me";
     // Do something here
    QGraphicsItem::mousePressEvent(event);
}

You dont need the QPushButton class for this...If you want to use your existing polygon items, you can make them clickable and react on mousePressEvent.

https://doc.qt.io/qt-5/qgraphicsitem.html#mousePressEvent

Anyway, you can change the painter from your QPushButton derived class to make it look like a polygon...but if you want to click your GraphicsView-Items, I would go with the first option.