I require a VPS with the mentioned specifications and my budget is limited to $10/month.

To minimize excessive bandwidth usage, why not consider switching to a dedicated server? By doing so, the entire 1gbps port will be solely dedicated and there would be no complaints about usage.
Realistically, with a budget of only $10 per month, an unlimited bandwidth on a dedicated server is impossible to obtain.

I regret to inform you that the mentioned specifications of 8 cores, 1gbps unmetered, 4GB RAM and SSD storage are not possible within your budget.

You can't buy anything sensible for that kind of money. Add money and buy a normal vps. You can find a powerful vps for $98 a month. And you can't buy anything for $10, especially now.

Due to the recent events of Covid-19 and what is happening around Russia, the price of service providers has increased. As for $10/month with these characteristics, I can't offer, but there are close ones in value:
https://contabo.com/en/vps/ -$7 (Cloud VPS S - 4 vCPU, 8 GB RAM, 200 GB SSD, 32 TB Traffic)
https://vpsfree.cz/ - $12.5 (8 Cores/4Gb Ram/120Hdd)
To be realistic, a good VPS with 8 cores starts at $44/mo.

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