Asia is a continent, not a country. No countries from Asia are members of the European Union. Cyprus is the country in the European Union that is furthest from Ireland.
Cyprus is the EU country that is furthest east.
The nearest EU country to Ireland is the United Kingdom. The UK borders directly on Ireland, as Northern Ireland is part of the UK.
Finland (Just) folowed by Sweden
One other country that joined the EU the same year as Ireland (1973) was Denmark.