Recent end-to-end automatic speech recognition (ASR) models have become increasingly larger, making them particularly challenging to be deployed on resource-constrained devices. Model quantisation is an effective solution that sometimes causes the word error rate (WER) to increase. In this paper, a novel strategy of personalisation for a quantised model (PQM) is proposed, which combines speaker adaptive training (SAT) with model quantisation to improve the performance of heavily compressed models. Specifically, PQM uses a 4-bit NormalFloat Quantisation (NF4) approach for model quantisation and low-rank adaptation (LoRA) for SAT. Experiments have been performed on the LibriSpeech and the TED-LIUM 3 corpora. Remarkably, with a 7x reduction in model size and 1% additional speaker-specific parameters, 15.1% and 23.3% relative WER reductions were achieved on quantised Whisper and Conformer-based attention-based encoder-decoder ASR models respectively, comparing to the original full precision models.