'Agius' is a relatively common surname in Malta. So if your surname is Agius it is unlikely that you will easily find a common ancestry with another 'Agius' who you may have come across at random. 

If you did wish to search for your ancestors, start by getting Public Registry civil status certificates, including Birth, Marriage and Death through certificates online. Get the 'complete' certificates. Unfortunately at present this service will only provide birth certificates as far back as 1863 (which is relatively recent in genealogical terms). To go further back you would need to try other means such as the church registers of the parish(es) where your ancestors were born or present yourself in person at the Public Registry office in Valletta. 

If you do not have the time and the knowledge that is needed, you might need to search for and engage the services of a genealogist.

The following web pages might also help.

Agius Family Home Page