[www.amazon.com/Historic-Print-Kleberg-Building-Kingsville/dp/B003HXIIY]

"OLD R.J. KLEBERG BANK BUILDING & CITY OF KINGSVILLE MUNICIPAL BUILDING
... In its original form, the R.J. Kleberg Bank was a staple in the making of Kingsville. Organized in 1905, it was the first bank in town and essentially funded the community's construction. The building's original wooden structure suffered an irreparable fire on New Year's Eve in 1909, however the vault containing the money and Bank's records remained safe, allowing the Bank to continue its business. The new building that stands today was completed and opened in 1910. Kleberg Bank occupied only the first floor of the building and rented out the extra space to several tenants throughout the years, including a drugstore, a meat market, a jewelry store, and offices for attorneys, doctors, a dentist, the Kingsville Land & Investment Company and the King Ranch. The Bank sold the building to the City of Kingsville for $125,000 in 1969 and the City of Kingsville moved in in 1971. Kleberg Bank moved across the street to the northwest corner of Kleberg Avenue and 6th Street where its main branch still operates today." [https://localwiki.org/kingsvilletx/Historic_Downtown_Kingsville] 

The First National Bank of Kingsville, charter 12968, was established July, 1926, and printed currency for the remainder of the National Bank period.
Although it is not explicitly stated, evidence indicates that The First National Bank of Kingsville was created by the conversion of the R. J. Kleberg Bank, pictured above.

The First National Bank of Kingsville printed 1902 Plain Backs and 1929 Types 1 & 2.

The National Bank Currency Census reports fifty-six notes from the First National Bank of Kingsville: eight 1902 Plain Backs, eighteen 1929 Type 1's, and thirty 1929 Type 2's. None of the 56 is in the Philpott-Moody Collection.

This Plain Back sold in September, 2015, at a Heritage Currency auction for $2,820.

[Image Heritage Currency Auctions]

"Kingsville, TX - $5 1902 Plain Back Fr. 609 The First NB Ch. # 12968
A double serial number 1 note from the sole National Bank chartered in Kleberg County, the site of the famous King Ranch. It is one of only two serial number 1 examples extant from this bank and is accompanied by an interesting letter from Cashier Sam Fimble, Jr. to his mother dated August 6, 1928. Mr. Fimble writes "Dear Mama- At last, enclosed you will find the said $5.00 bill, one of the first our bank issued or made. We started our circulation account on Saturday, July 28, 1928 and issued $50,000.00 of these five dollar bills and now have this money scattered over Corpus Christi, Robstown, Bishop, Kingsville and South Texas. There will be no more number one bills so put this one away. If you ever want to get rid of it, then I will buy this one back." Mr. Fimble...tonight is your chance. PCGS Apparent Choice About New 58, with a repair at the left edge and some very minor discoloration on the reverse."