Looking for Guidance in Breaking into Banking

Hi everyone,

I'm an international student nearing the end of my third year at a non-target liberal arts college in the US studying mathematics and economics. During my third year, I spent a year abroad at the London School of Economics (LSE), where I took some advanced finance courses which piqued my interest in a finance career. I have been exploring a career in finance, but I'm still unsure of the specific field that best suits me.  Ideally, I'd like a role with a good mix of quantitative analysis and daily variation, but I understand something like quantitative research might be too demanding at this stage.

The challenge I face is my lack of experience. While I applied for various internships in banking (trading, wealth management, portfolio management), I haven't landed any yet. Though I have had internships in the past, they have been at my home country and have informal. My upcoming summer internship is in the strategy department of a prominent telecom company in the Middle East and Africa region, which is valuable but not directly related to banking.

To bridge this gap and gain a foothold in banking, I'm looking for advice in several areas:

• Recommendations for Banking Fields: Given my background and interests, what specific areas within banking would you recommend I explore further? Are there particular banking sectors you'd recommend for someone with my profile?
• Strategies for Landing a Full-Time Role: What specific steps can I take during my summer and fourth year to increase my chances of landing a full-time banking position upon graduation? 
• Preparation: How can I best prepare myself for potential applications and interviews in the coming year? Any resources or suggestions on building relevant skills would be greatly appreciated.
• Fall Semester Internship Opportunities: Ideally, I'd like to find a part-time, remote internship in finance for the fall semester to further my experience. Does anyone have any leads or advice on how to find such opportunities?

I'm feeling a bit lost, and any guidance or mentorship would be incredibly valuable. Thank you for your time and support!