You need not to be a Canadian citizen or immigrant.
If you are a resident of Canada for "tax purposes". You may apply the "Canada Child Tax Benefit (CCTB)" and "Universial Child Care Benefit (UCCB)" from Government of Canada
Also,
Ontario Child Benefit (OCB) 牛奶金, from Ontario government.
Note:
- CCTB and OCB are for 'low income family' and they have family income limit. (about $25,000 depending on the number of children)
- UCCB has no family income limit and it pays to family (usually mother) with child(ren) under 6 years old.