Medical dictation systems are essential tools in modern healthcare, enabling accurate and efficient conversion of speech into written medical documentation. The main objective of this paper is to create a domain-specific system for Greek medical speech transcriptions. The ultimate goal is to assist healthcare professionals by reducing the overload of manual documentation and improving workflow efficiency. Towards this goal, we develop a system that combines automatic speech recognition techniques with text correction model, allowing better handling of domain-specific terminology and linguistic variations in Greek. Our approach leverages both acoustic and textual modeling to create more realistic and reliable transcriptions. We focused on adapting existing language and speech technologies to the Greek medical context, addressing challenges such as complex medical terminology and linguistic inconsistencies. Through domain-specific fine-tuning, our system achieves more accurate and coherent transcriptions, contributing to the development of practical language technologies for the Greek healthcare sector.