Do you know any Java cookie implementation which allows to set a custom flag for cookie, like SameSite=strict? It seems that javax.servlet.http.Cookie has a strictly limited set of flags which can be added.
I am not a JEE expert, but I think that because that cookie property is a somewhat new invention, you cannot expect it to be present in Java EE 7 interfaces or implementations. The Cookie class is missing a setter for generic properties, as it seems. But instead of adding the cookie to your HttpServletResponse via
response.addCookie(myCookie)
you can simply set the corresponding HTTP header field via
response.setHeader("Set-Cookie", "key=value; HttpOnly; SameSite=strict")
Update: Thanks to @mwyrzyk for pointing out that setHeader() overwrites all existing headers of the same name. So if you happen have other Set-Cookie headers in your response already, of course you would use addHeader() with the same parameters instead.