On-device machine learning is becoming a reality thanks to the availability of powerful hardware and model compression techniques. Typically, these models are pretrained on large GPU clusters and have enough parameters to generalise across a wide variety of inputs. In this work, we observe that a much smaller, personalised model can be employed to fit a specific scenario, resulting in both higher accuracy and faster execution. Nevertheless, on-device training is extremely challenging, imposing excessive computational and memory requirements even for flagship smartphones. At the same time, on-device data availability might be limited and samples are most frequently unlabelled. To this end, we introduce PersEPhonEE, a framework that attaches early exits on the model and personalises them on-device. These allow the model to progressively bypass a larger part of the computation as more personalised data become available. Moreover, we introduce an efficient on-device algorithm that trains the early exits in a semi-supervised manner at a fraction of the whole network's personalisation time. Results show that PersEPhonEE boosts accuracy by up to 15.9% while dropping the training cost by up to 2.2x and inference latency by 2.2-3.2x on average for the same accuracy, depending on the availability of labels on-device.