Case is a Texas case, but Defendant is currently in New York and doing business in Texas from New York. The citation was sent to TExas-SOS citations unit who forwarded it to Defendant's listed office and registered agent in New York. However the defendant did not accept the certified maail and it returned. The Texas SOS sent the Whitney Certificate mentioned the mail was undelivered as nobody accepted the mail. Is this Certificate which shows that the Defendant did not accept the mail enough proof of Service? Will that be sufficient for Texas State court to Satisfy Service of Process requirement?
If the Defendant is a corporation doing business in Texas, and it does not have a registered agent in Texas, then the Secretary of State is their agent for service of process. In that case, service is effective when it's delivered to the Secretary of State, even if the mail from the Secretary of State ultimately not picked up.
In order to get the court to enter the default judgment, you'll have to satisfy the judge that the defendant was doing business in Texas, and does not have a registered agent in Texas.
Medical Malpractice Attorney
Effecting service on a defendant under the Texas long-arm statute, which is what you are describing, is highly technical. The judge will require strict adherence to the applicable procedural rules before he or she grants you a default judgment in the event the defendant fails to answer timely. Accordingly, if you don't have a lawyer, I stongly suggest that you hire one. Even if you get a default judgment, that is only a piece of paper. Converting that piece of paper into money requires a formal legal education, as well as training and experience in collecting judgments. This is particularly true where, as here, the defendant resides is a state different from the one in which the court renders judgment.