Said piece of land goes across the end of my driveway and, and has been used for parking by residents of my property for at least the last 30 years. I bought here 7 years ago. It also allows access to my private gravel driveway, that I made very clear 7 years ago that was not for use by anyone other than my family and guests. Period. I even went so far as to put up a gate and partial fencing of my gravel driveway to block access but I continue to have problems with them using my drive. Can I take this small area of land so I can put up a fence and permanently stop this trespassing. I know if I just put up a fence my neighbor wouldn't stand for that. But my family and friends, and even myself regularly park there and have for 7 years.
You may have a problem establishing an adverse possession claim if your use of the are has not been exclusive - in other words, the fact that your neighbors are using the area, too, may hurt your case. You need to talk to a lawyer in your area who is familiar with adverse possession.
Adverse possession is a common law concept, and does not apply in Louisiana. The closest Louisiana concept is acquisitive prescription. Louisiana Civil Code Article 3476 provides:
"The possessor must have corporeal possession, or civil possession preceded by corporeal possession, to acquire a thing by prescription.
The possession must be continuous, uninterrupted, peaceable, public, and unequivocal."
For a person acting in good faith -- that is, the person thinks he actually is the owner of the land -- the period needed to acquire the land is 10 years; for a person not acting in good faith, the period is 30 years. From your description, it appears that your situation fails to meet the requirements for acquisitive prescription.