I work in HFT, and I'll be contrary and suggest that if you want the most value from your time, focus on learning as much maths and probability as possible. Once you have a strong maths background, learning most financial maths is relatively easy. Any of the financial models you find in textbooks are probably useless because if they work, everybody else who's read the textbook has also used them so there's unlikely to be any edge left, hence it's the ideas underneath them that matter, and understanding and extending these is much easier with a strong maths background. The key skill is developing and assessing new models, and the better one's maths, the easier this is (imagine if a market behaved like a complex aerodynamic system; only somebody with enough mathematical background to model a complex aerodynamic system would be able to create a very accurate model of that market).
One of the most successful hedge funds, Renaissance Technologies, also takes this approach. Regarding its employees: "a third have PhDs, not in finance, but in fields like physics, mathematics and statistics. Renaissance has been called “the best physics and mathematics department in the world” and, according to Weatherall, “avoids hiring anyone with even the slightest whiff of Wall Street bona fides." (https://en.wikipedia.org/wiki/Renaissance_Technologies). Similarly some of the best HFT hires I've been have been people with a maths or science background.
A quote sourced to Renaissance Technologies from https://www.quora.com/What-is-the-secret-behind-Renaissance-...: "We have some Tier One mathematicians and a lot of Tier Two mathematicians. Other quants funds have mostly Tier Three mathematicians, and worse, they don’t even know that these tiers exist! Someone has to create the correlations in the markets." Aim to be one of those Tier one mathematicians!
One of the most successful hedge funds, Renaissance Technologies, also takes this approach. Regarding its employees: "a third have PhDs, not in finance, but in fields like physics, mathematics and statistics. Renaissance has been called “the best physics and mathematics department in the world” and, according to Weatherall, “avoids hiring anyone with even the slightest whiff of Wall Street bona fides." (https://en.wikipedia.org/wiki/Renaissance_Technologies). Similarly some of the best HFT hires I've been have been people with a maths or science background.
A quote sourced to Renaissance Technologies from https://www.quora.com/What-is-the-secret-behind-Renaissance-...: "We have some Tier One mathematicians and a lot of Tier Two mathematicians. Other quants funds have mostly Tier Three mathematicians, and worse, they don’t even know that these tiers exist! Someone has to create the correlations in the markets." Aim to be one of those Tier one mathematicians!