I am not aware that there is any specified minimum distance between "No Trespassing" signs in Texas. You might get some guidance from Section 30.05 (Criminal Trespass) of the Texas Penal Code, which states (in part):
(a) A person commits an offense if the person enters or remains on or in property of another, including residential land, agricultural land, a recreational vehicle park, a building, or an aircraft or other vehicle, without effective consent and the person:
(1) had notice that the entry was forbidden; or
(2) received notice to depart but failed to do so.
(b) For purposes of this section:
(1) "Entry" means the intrusion of the entire body.
(2) "Notice" means:
(A) oral or written communication by the owner or someone with apparent
authority to act for the owner;
(B) fencing or other enclosure obviously designed to exclude intruders or
to contain livestock;
(C) a sign or signs posted on the property or at the entrance to the building,
reasonably likely to come to the attention of intruders, indicating that entry
(D) the placement of identifying purple paint marks on trees or posts on the
property, provided that the marks are:
(i) vertical lines of not less than eight inches in length and not less than one
inch in width;
(ii) placed so that the bottom of the mark is not less than three feet from
the ground or more than five feet from the ground; and
(iii) placed at locations that are readily visible to any person approaching the
property and no more than:
(a) 100 feet apart on forest land; or
(b) 1,000 feet apart on land other than forest land; or
(E) the visible presence on the property of a crop grown for human consumption
that is under cultivation, in the process of being harvested, or marketable if
harvested at the time of entry.
(the statute goes on with additional definitions and to describe other details, including exceptions and penalties).
To be safe, and unless someone else posts a response indicating that there are specific distance requirements for these signs, my recommendation would be to place the signs close enough to each other that a reasonable person could not say that a sign was not visible to him from any location immediately adjacent to your property.
DISCLAIMER: The information provided in this post is general information only and is not intended to be, nor is it, specific legal advice for the facts cited or for any similar facts. The reader is encouraged to seek the assistance of a lawyer to assess the complete set of facts and provide legal advise thereon. This post does not establish any attorney/client relationship, either with the person who submitted the actual question or any other person.