Abstract: A gas cock for a gas burner and pilot flame includes a cock body with a plug receiving seat and a gas passage opening for passage of gas from/to the plug receiving seat. The cock has a conical plug, including a side wall extending around a central conical plug axis and housed in the plug receiving seat. The conical plug includes a plug opening for passage of gas from/to the plug receiving seat by the inner cavity of the conical plug based on a presettable angle of rotation between the cock body and the conical plug. The conical plug outer wall surface includes a groove connected to the plug opening. The groove includes a modulating portion extending between first and second angular positions in a circumferential direction of rotation of the conical plug with a depth that increases or decreases in the radial direction perpendicular to the side wall.