I think that may be a bad transmission of the name Pedro de Paz, who was a famous captain, a man of the utmost trust of Gonzalo Fernández de Córdoba and of the Catholic Monarch. Nowhere have I seen mentioned that he was a dwarf, however it is said that he was somewhat hunchbacked and short. As it always happens, Gonzalo Fernández de Oviedo personally knew the famous captain, and mentions him in his Batallas y Quinquágenas. I'll translate:

Sereno - I knew captain Pedro de Paz, and saw him many times, of bad disposition of his bodily presence, but full of virtues, a man of great effort, and I think he died in the battle of Ravenna.

Alcayde- He was so valorous and virtuous that even with his bad size and ugly disposition he made himself remarkable and advantaged, and in his daring, and virtue, and military prowess was on par with the most famous knights. And in spite of him being short in stature and somewhat hunchy, and not of a good face or well made, as I say, his lance was amongst the best, and his dilligence and effort are worthy of being remembered among the most famous captains of his time. He was in the wars of Naples in the time of the Great Captain and did remarkable things, and his person was held in high esteem, for his ability in the military art was much, and besides this he talked very well, and was wise and naturally virtuous.

Pedro de Paz was such a memorable knight that Ferdinand the Catholic nicknamed him "Fear Taker", for he was so sagacious in the art of war that no soldier under his command feared for his life.

Captain Pedro de Paz indeed took part in the battle of the Garigliano river, where he was put in command of defending one of the bridges with 1,200 infantry soldiers, but the French artillery forced him to retreat to the other side of the river where he set up trenches with some reinforcements commanded by Alonso de Carvajal consisting of 200 light cavalry troops. After the battle was won, Pedro de Paz was put in charge of a small force tasked with pursuing the French forces that were fleeing.

u/TywinDeVillena has given the bulk of the answer about Pedro de Paz from the Spanish perspective. In the context of the Bayard legend, the character appears in the main biography of the French knight, published in 1527 by "The Loyal Servant", believed to be Jacques de Mailles, possibly the personal secretary of the Knight (and later notary of the Bayard family). The text goes as follows (English translation of 1825; French version of 1878):

It must be understood, that, if there were good and valiant Captains among the French, such were likewise to be found on the side of the Spaniards; amid others, the great Captain Gonsalvo of Cordoba, a wise and vigilant man, with another named Pedro de Paes [de Pas in the original French version], who was not three feet high [deux couldées], but as brave a creature as you could any where find. He was so little and so hunch backed [fort bossu et si petit] that when he rode you could see nothing but his head above the saddle. One day the said Pedro de Paes took it into his head that he would give an alarm to the French, and, with an hundred or an hundred and twenty horse, he set about crossing the Garigliano in a certain place, where he was acquainted with the ford, and had placed behind each horse a footsoldier furnished with an arquebuse. He gave this alarm in order that the army might run thither, abandoning the bridge, while the Spanish force was arriving; and this he carried into effect. He executed his enterprise very well, and raised a sudden and violent alarm in the camp of the French, whither they all retired, thinking the Spaniards were about to make no further effort; but they were deceived.

A few pages earlier, Bayard and de Paz have a very courtly interaction:

[de Paz] "On my honour, my Lord of Bayard, although I know full well that we have gained nothing by your arrival, but, on the contrary, hold your camp two thousand men the stronger thereby, nevertheless I am right glad to see you; and would God there were peace between your master and mine, in order that we might have a little discourse together: for I have loved you for your prowess all my life." The good Knight, who in courtesy was surpassed by no one, answered him in the same or a more complimentary strain.

Jacques de Mailles' biography is more hagiography than history (though he did witness some of the events he describes), and he took elements from a previous biography written by Symphorien Champier in 1525 (writing biographies of celebrities was already a competitive editorial business). His book was titled The right joyous and pleasant history of the feats, gests, and prowesses of the Chevalier Bayard, the good knight without fear and without reproach. Because it is relatively well-written and entertaining, it has been for five centuries the go-to source for Bayard stories, notably when the Good Knight entered the French Roman national in the 19th century, and has long been a popular book translated in other languages. This is why the "Pedro de Paz, hunchback" is still associated to Bayard. Since both de Mailles and the Spanish sources describe Pedro de Paz as (very) short, brave, smart, and knightly - basically a real-life Tyrion Lannister -, there seems to be a nugget of truth there, with Mailles' "hunchback" only a creative exaggeration and a way to introduce the amusing image of a knight whose head was just "above the saddle".