Upon the trial of any such action, either party may give in evidence the statement mentioned in Section 19-4-10 N.M. Stat. Ann., deposited by the other, or by the person under whom he, or she, claims, with the corporate authorities or probate judge. And the person, or persons, who shall have first acquired the right to the possession, or occupancy, of such lands, either in person, or by agent, servant or tenant, or those claiming under him, her or them, shall be deemed to have the prior and paramount right to such lands: provided, that nothing in this section shall be so construed to recognize the right of any person or persons who have virtually abandoned any land held as a townsite, to any title therein.