You could, however, there are certain conditions you need to meet.
If you want to sponsor a nephew, you should keep this in mind:
You can sponsor an orphaned brother, sister, nephew, niece or grandchild only if they meet all of these conditions:
- they’re related to you by blood or adoption
- both their mother and father passed away
- they’re under 18 years of age
- they’re single (not married or in a common-law or conjugal relationship)
You can’t sponsor your brother, sister, nephew, niece or grandchild if:
- one of their parents is still alive
- no one knows where their parents are
- their parents abandoned them
- someone else other than their parents is taking care of them while one or both their parents are alive
- their parent is in jail or otherwise detained
Based on the little information you provided it seems you would not be able to do so.
Regarding your mom's cousin, I highly doubt you could somehow prove this relationship. And to be honest, you can't consider your mom's cousin as your relative (at least medically not).
Are your parents alive? Are you married?
I would suggest reading this and assess your situation accordingly: https://www.canada.ca/en/immigratio...ship/other-relatives/who-you-can-sponsor.html
