A method and a device in a UE and a base station used for wireless communication are provided. First information and a first target signal are received, the first information indicates a listening type; it's determined whether a first time-frequency resource is used for wireless transmission based on the listening type indicated by the first information; if yes, a first radio signal is transmitted with a first power on the first time-frequency resource; wherein if the listening type indicated by the first information is a first listening type, the first power cannot exceed a first maximum transmitting power, receiving quality of the first target signal is used for determining the first maximum transmitting power; if the listening type indicated by the first information is a second listening type, the first power cannot exceed a second maximum transmitting power. The method ensures equity and improves transmission efficiency and spectral utilization ratio.