Are you using the regular txt program on the phone or a downloaded one? If it's a downloaded one..some of them back up the txt. If it's the regular txt app on your iphone then I believe the only way would be if you had backed up the phone to itunes or icloud in the timeframe you had the messages on the phone. If they were backed up you can restore from itunes/cloud but that will delete your current info.
@Johndeere1 Generally, you would have to have access to the phone itself. Text messages are considered private and will not be posted on your online account. If you are an account owner, you may be able to see messaging detail such as time and date sent within the myverizon website, but you won't be able to see the content of the message.