Is it permitted to give money earned from interest towards marriage of Aunt's daughter (mothers side) as they are poor; we are not expecting any sawab from this.

At the outset, we wish to inform you that to earn money from interest is Haraam and strictly prohibited.

You should not give it towards the marriage specifically. Rather give it to them to fulfil their needs. This will only be permissible to give to them if they are so poor that they are deserving of Zakaat.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai