Is it permissible to accept a financial prize and a certificate of appreciation from an economic competition organized by an entity suspected of dealing in usury, knowing that the submitted research does not advocate anything contrary to Sharia?

If the subject of the competition is permissible and its prize is lawful, unless it is highly probable that the provider is an interest-based bank, then the issue falls under the ruling of dealing with someone whose money is unlawful. If all of their money is unlawful, then dealing with them is forbidden. If the majority or most of it is unlawful, then dealing with them is disliked. Nevertheless, it is not forbidden to benefit from the prize if it is given to you, though refraining from it is more virtuous. However, it can be taken and benefited from, or given to the poor and needy out of piety.