Not sure if it is what you are looking for since California was a state at the time of the Civil War, but there was for a time a California Brigade with the Army of the Potomac, though the majority of the recruits came from the city of Philadelphia. After the battle of Ball's Bluff however Pennsylvania claimed the brigade, the regiments were renamed to Pennsylvania regiments, and the California Brigade became the Philadelphia Brigade.
Their brightest moment in the war was at the Angle on the 3rd Day of Gettysburg, where the 69th and 72nd Pennsylvania (formerly the 2nd and 3rd California) held out against elements of Armistead's brigade in bitter fighting.
The California Brigade
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In West Philadelphia Born and Raised
Daniel Landsman
When the Civil War broke out, residents of the west coast wanted to have a presence in the eastern theater. However, with nearly 3,000 miles separating the state of California and the Army of the Potomac and no railroad connecting the west coast to the east, sending a brigade of infantrymen across the wild country would be an ambitious goal. Instead, a group of Californians asked Oregon Senator Edward Baker to head east and raise a brigade in the name of California.
Oregon Senator Edward Baker went to Pennsylvania to raise a brigade in the name of California.
Library of Congress
In April 1861, Baker was commissioned by Abraham Lincoln to raise a California brigade in Philadelphia. The first regiment Baker organized, the 1st California, consisted of Philadelphians and was placed under immediate charge of Colonel Isaac Wistar, who had been a ranger in California during the 1850s. By October Baker’s brigade had grown to its full size, consisting of the 1st, 2nd, 3rd, and 5th California Infantry.
The 3rd California had another name at the time of conception. Known as the Philadelphia Fire Zouaves, the men of the 3rd California were easily recognizable by their uniforms, which were inspired by the Zouaves of the French army. Dressed in light blue pants cut wide with red stripes and a cut away jacket with a row of bright blue buttons, the Philadelphia Fire Zouaves drew considerable attention as they marched through the streets of Philadelphia.
The rest here:
https://www.battlefields.org/learn/articles/california-brigade