gANesa have many avatAra’s, as per mudgalA pUraNa [8 avatAra's] mUSaka is His vAhana in only five of them. As vakratuNDa [वक्रतुण्ड ] he rides a lion [सिंह वाहन - siMha vAhana] in His next avatAra - vikaTa [विकट] , He rides a mAyUra[मायूर] and during His vighnarAj avatAra [विघ्नराज्[ seSa [शेष divine serpent] is present with him. Some of the ancient, old depictions of gANesa don’t show a vAhana with Him at all and only somewhere around late 6th century – early 7th century the vAhana was connected in the depictions. Oldest gANesa statues are found in South East Asian countries like Indonesia and Laos did not havemouse [मूषक] as vAhana.
Ganesha Purana [गणेश पुराणम्; gaṇeśa purāṇam] mentions Mahotkata Vinayaka vAhana as either an elephant [गज] or lion[सिंह]. While Mayuresvara has peacock [मायूर] and Gajanana mount was a mouse [मूषक] . gANesa final avatar in Kaliyug, Dhumraketu has a blue horse [नीलअश्व]. मूषक [mouse] is the vAhana in Matsya Purana and the Brahmananda Purana. One of gANesa names is Akhuketana /आखु केतन [ -आखु - mouse and केतन -flag] Jainism connects gANesa with mouse [मूषक], elephant [गज] , tortoise [कूर्म], ram [मेष]or peacock [मायूर].