I have tried to google for info but can’t find any. As the question says, I am trying to find out if there was the concept of paternity leave in Spain during 1913 and, if so, how long for?
No, at least not officially. Paternity leave wasn't first legislated for in Spain until 1980, when fathers were given two days' leave (or four days if the child died). In 1989, this was extended to four days and in 2007 to 15 days. Note that, historically, maternity leave evolved in large part as a response to health concerns related to childbirth (i.e. fathers didn't give birth so there was no issue here).
Paternity leave in the West was introduced in the 1970s in Scandinavian countries, partly in response to the greater number of women entering the work force. Also, there was a groundbreaking case in New York in 1973 when:
the EEOC [Equal Employment Opportunity Commission] “found that the mothers-only rule ‘discriminates against male teachers as a class.’ As a result, the board says it will reword its bylaws to ensure equal rights for fathers.” That autumn, the relevant section of the Board of Ed bylaws was amended so that it no longer referred to an affected teacher as “her” or relied on the timing of the teacher’s pregnancy, thus expanding its relevancy to fathers and to adoptive parents. The determination is widely regarded as the groundbreaking first step toward paternity leave’s existence.
In Spain, men had very little opportunity for paternity leave until 2007:
The first paternity law reforms came in 2007 via the Spanish Law on Gender Equality which introduced a non-transferable, two-week paternity leave with a 100% wage compensation, followed by other expansions, adjustments and improvements over the years.
Note that even maternity leave was uncommon before the 20th century. Switzerland seems to have been the first country by some distance when
The Swiss Factory Act of 1877 provided an 8-week ‘rest period’ for mothers, six of which had to follow birth.
Germany also introduced a form of maternity leave before 1900 while, in Spain, maternity leave came about in 1900, when three weeks of leave was granted.
Note: the information on Spain comes from articles in Spanish, for which I used google translate.