Really sorry OP, but there is no legitimate route for Syrians to come to the UK for protection purposes and be sponsored in the way you describe. The only safe and legal routes for refugees are the Ukrainian visa, ARAP (the Afghan relocation and assistance policy) and the Hong Kong British National overseas route. It's awful and I'm sorry.
The UK previously had a programme called the Syrian Vulnerable Persons Resettlement Scheme, which brought in around 20,000 refugees to the UK but it was done in conjunction with the UNHCR, who identified vulnerable Syrians and referred them directly to the Home Office. It wasn't an open scheme like the ones above, and it closed in 2021. It was replaced with something called the UK Resettlement Scheme, but this is global, not just for Syrians, and it has only resulted in a tiny amount of people coming to the UK so far. It is also administered by the UNHCR (you need to register with them, but you can't 'apply' for it - they select people based on need) and you need to already be a recognised refugee. It's normally people who are particularly vulnerable or who have severe health needs who are referred.
Does your mother need long-term care to do everyday personal and household tasks because of illness, disability or age, and if so, can she prove it? There is something called a Family Visa but it has strict criteria, and you can only apply as the parent of an adult child if you need care as per above. You, as the child, must also have indefinite leave to remain, or protection status. It will cost several thousand, plus another £2–3k to use the NHS, and will probably take months but if it's a possibility the details are here: https://www.gov.uk/uk-family-visa
Really unlikely to be granted a standard visitor visa in the current circumstances.
I wish you both all the luck in the world.