"has possibly" is correct and can be used in written English.
You can use it when you are suggesting that something might be true, but you are not certain. For example: "It has possibly been raining all night."
Growing older has possibly come as something of a relief.
Forty-two of the most restrained, composed runs he has possibly scored in his life.
Another – a biopic, this time – has possibly the most heavily foreshadowed death scene of all time.
Girma Seifu Maru has possibly the loneliest job in African politics.
She has possibly laid the foundation for a guerilla war in Punjab.
"It has possibly been hit by a boat or propellers and that has caused severe damage.
"It could be nothing but this patient has possibly been at risk," he added.
The guy is so tall and he has possibly the best serve on the tour.
"This ass," he said, indicating the donkey, "was meant for Polly, who has possibly made an ass of herself by not marrying when she could, or who has possibly made an ass of her would-be husband by refusing him.
Fans of Carl Hiaasen's crime novel Skin Tight might also feel that Black has possibly read Hiaasen's work.
And yet this forty-one-year-old painter has possibly given more interviews than any other contemporary artist.
