Q: if someone owned a small business and you are co-president of the company and he dies with a non signed witness will,

A: Almost nothing in your description is relevant to answering your question. You need to sit down with a lawyer, describe the assets in a manner cognizable at law, and determine where you stand legally. Many lawyers offer consults by Zoom from the convenience of your home of office.

A: Your use of pronouns "someone", "you", "he" and "I" is beyond confusing. It is unclear who these pronouns are referring to, other than the "I."

I'll take a stab: the owner of the company died without a will, and you are "co-president" of the company but not an owner. Is that it? If so, then here is what I can say about that without any other information:

It matters whether the business is a corporation, a limited liability company (LLC), a partnership or a sole proprietorship. You do not say. When someone dies who is the sole shareholder of a corporation, or the sole member of a limted liability company, or the sole owner of a sole proprietorship, and they do not have a will, their ownership rights pass to their heirs at law (spouse and children, or if none, then parents, siblings, etc.). But first the business is an asset of the deceased owner's estate, and it is either transferred to the heirs, or it is sold and the proceeds replace it as an asset of the estate for distribution to the heirs. An estate needs to be opened, and a personal representative appointed. If the business is organized as an LLC, the PR can only operate or manage the LLC for a brief window of time (90 days) to either sell or admit a new member to take over, or the LLC gets dissolved, and its assets added to the estate for distribution to the heirs.

What rights you have, as a non-owner, depends on whether you have an employment or other agreement in place, and how established the business is in terms of its operations and cash flow (e.g., is there a solid ongoing business with employees, customers/clients, revenues, payroll account paying salaries, etc.?). Are you now the key employee, the glue that holds the business together, who knows how its run and the only one capable of managing its affairs and keep it going? If so, that gives you leverage and perhaps makes you the best candidate to purchase the business from the estate, or to negotiate with the eventual new owner to keep you on as the person running it at a salary you are willing to accept to do it. But you do not become the owner or gain rights to take profits from the company after the death of the sole owner, unless and until you negotiate a buyout of the business from the PR of the estate. Meet with a lawyer and review the situation.