Redmi Phone Keeps Cycling Between the Logo and Fastboot

This sounds like a boot loop, and since it reaches Fastboot on its own, check whether the volume-down or power button is stuck or being pressed by the case. Remove the case, disconnect any charger, and try holding the power button for 15–20 seconds. If it still loops, try entering Recovery mode and clearing the cache if that option is available. A factory reset may fix a software problem, but it will erase the phone’s data, so only use it as a last resort. If the buttons aren’t stuck and Recovery won’t help, the battery or another hardware component may need repair.