Final answer:
Santa Fe, New Mexico was never a legitimate part of Texas, despite attempts by Texas to control the area. It became part of the United States directly through the Treaty of Guadalupe Hidalgo after the Mexican-American War.
Step-by-step explanation:
The region of Santa Fe, New Mexico never became part of Texas. Throughout the period of Texas's independence (1836–1845), there were attempts by Texas to claim territories to the west, including parts of what is now New Mexico. Notably, Texas forces made expeditions into the area around Santa Fe in an attempt to exert control over parts of New Mexico.
However, these incursions were ultimately unsuccessful, and Texas did not gain control of Santa Fe or any part of New Mexico. Following the annexation of Texas to the United States in 1845 and the subsequent Mexican-American War (1846–1848), the dispute over the southwestern border was resolved. The war ended with the Treaty of Guadalupe Hidalgo, in which Mexico ceded vast territories to the United States, including what is now New Mexico, but these lands were never a legitimate part of Texas. Santa Fe, as part of the ceded territories, became a part of the United States, but as a separate entity from Texas.