Here are some examples:
* "He proudly possesses a vast collection of antique coins." (Describes the manner of possession)
* "She secretly possesses a hidden talent for painting." (Describes the way possession is kept)
* "They jointly possess the property." (Describes the way possession is shared)
* "The company fully possesses the necessary licenses." (Describes the extent of possession)
Instead of looking for a direct adverb, consider what you want to emphasize about the action of possessing. Then, choose an adverb that best describes that aspect.