@SGaist I am not using Labview's serial port directly because of my code contain many background functionalities. It will take time to implement all in Labview. We want to just give readable data and few User interface to Labview. So user can directly use readable value and interface in Labview.

Ok,
I found the bullshit. My first try was setStyleSheet("background-color: myColor;"). As it did not work (no border when checked), I tried after setStyleSheet("QToolButton {background-color: myColor;}"). As it was still the same shit, and as the documentation recommends to set the border, I have moved to setStyleSheet("QToolButton {background-color: myColor; border:none;}") (as in the QSS file). And all the following tries were with "border:none" on the rule without the :checked modifier.

Suprisingly, without the definition of the border in the setStyleSheet everything works well. So I have the border defined in the QSS file (as from the beginning). And in the program I have:

currentBtn ->setStyleSheet(QString("QToolButton#BooleanObject {background-color: %1;} QToolButton#BooleanObject:checked {background-color:%1;}").arg(myColor.name()));

This is a really strange behavior. But, long time ago, I have understood that I will never understand the "logic" of the QT style sheet.