I finally found a solution to this situation.
Accidentally, I found a method in Twitter SDK Kit for Android
CookieSyncManager.createInstance(this);
CookieManager cookieManager = CookieManager.getInstance();
cookieManager.removeSessionCookie();
Twitter.getSessionManager().clearActiveSession();
Twitter.logOut();
This was very simple, it took me about half an hour to find it.
For version 3.0 and above
CookieSyncManager.createInstance(this);
CookieManager cookieManager = CookieManager.getInstance();
cookieManager.removeSessionCookie();
TwitterCore.getInstance().getSessionManager().clearActiveSession()
Browser.clearHistory(getContentResolver());
, still the same issue – Saadi