As a refugee claimant in Canada, you are allowed to travel within the country while your claim is being processed. You are not restricted to staying in one province or territory. You can travel freely from Ontario to Alberta or any other province or territory in Canada.
However, it's important to keep in mind that you are required to attend all scheduled appointments with the immigration authorities, such as interviews or hearings, and to inform them of any changes to your contact information, including a change of address. If you plan to travel outside of the province where your claim was made, it's a good idea to inform the immigration authorities of your plans and to keep them updated on your whereabouts.
It's also important to be aware that if your claim is ultimately rejected, you may become subject to removal from Canada. In that case, it's important to seek advice from a qualified immigration professional, who can help you understand your options and assist you with any necessary steps.