What would you bring with you to the past to pove to people time travel is real?

Depending how far back I am going, my smartphone would be sufficient. Even without any kind of connection, it can do some rad stuff that would blow the minds of anyone in the 90's or earlier.
- Take a photo of them. Then zoom in. If that doesn't blow their minds, take a video of them and play it back.
  Digital cameras have been commercially available as early as the late 80s, but were of course super low res and with terrible image quality even accounting for that compared to what I just carry in my pocket now.
- Charging wouldn't be that difficult either if its pre USB-C. A nice steady 5V trickle at two visible connectors. Get yourself a nice thin copper wire with the right number of turns along a rotating magnet, and crank that handle gently

Assuming we're going back far enough, antibiotics. Cure one person of the bubonic plague or tuberculosis and people will start taking you seriously.
- Burn the witch!!!
- Often wondered how much mileage one could get out of moldy bread. This looks promising, haven't read it all.
  https://www.reddit.com/r/askscience/comments/ubrekq/before_flemings_accidental_discovery_of/

I would bring a list of supernovas that occured in my past, but in the future of the time I traveled to. A couple matching observations will provide indisputable proof that I have information from the future.
- At first I thought you talked about Hiroshima and Nagasaki. Been a while since I heard Supernova for it's actual meaning o_o
  
  I've never heard a nuclear bombing described as a supernova, but you do you?

I'd bring a scientist with me. Not sure which one. Just grab one with a cloth sack when they're having breakfast with their kids, and stuff em into my time machine. They'll figure it out.
Then I'd prod them to do future math and stuff for peasant farmers.
- Then the peasant farmers either burn you both for witchcraft or shun you as the village idiot rambling about nonsense.
  
  But... but... The Taylor Series expansions!

I have a recurring fantasy of visiting my favorite physics professor in the 1970s and showing him a modern smartphone. He showed me how to use integrated circuits, when microprocessors were a very new thing and we were mostly just making LEDs blink.
- Came to say cell phone. Even as recently as the early 90s, no one on Earth had tech that was close. It would be plenty understandable by extrapolating current tech, but no one would believe it was a contemporary device.
  
  Yep exactly. Many people in 1975 might have thought a smartphone was some kind of trick, but the professor I'm thinking of was very familiar with digital electronics and would know it was absolutely impossible to build such a thing at that time. I would really love to tell him all about the Internet etc. And of course when to sell his house and buy Microsoft stock lol.

Generator. Television. PS2. Cowboy Bebop on DVD.
Idk if it would work at all, but TANK is such a good fucking song, and I hope they enjoy at least that much before burning me for witchcraft.

How far back are we talking?
I mean the 90s were about 30 years ago (sorry for making you feel old).
So let's say that that I managed to find a way to travel in time, and had time to prepare for a trip to 95...
I will also assume that it is a paradox self correcting time travel deal.
I'd bring an iPhone with me, that should convince anyone that I am from the future.

A fixed gear bicycle with wide, flat-resistant tires and a belt drive. Plus a hand pump, a set of tools and a box full of inner tubes.
That should be enough to keep it running for a lifetime, offers actual utility, and it's understandable enough what it does so I'm hopefully not burnt at the stake, and people can build their own with what they have.

I would bury a bunch of identical time capsules all over the world, each with the location of the other time capsules and a detailed timeline of increasingly terrible global events.
The later it's dug up, the more credible it'll be.

A list of everything the church has ever had to walk back(they classified capybaras as fish), along with the scientific proof. And a thousand doses of Keflex.
- Bring the Keflex to save your own ass, if nothing else.

Why would I want to prove that it is real. I'd go full Connecticut Yankee and build a modern empire with me at the head.

I'd want something that can help people and can be tested and has an immediate, dramatic effect to make it undeniable
Maybe insulin? You could literally bring comatose people back from the brink of death in minutes
- Wouldn't anyone needing insulin already be dead? Or is there a middle ground where a diabetic can go in and out of shock, yet survive without?
  
  They would survive for awhile after diagnosis on a starvation diet, maybe weeks, and slipping in and out of a coma but it was a death sentence. There's stories from the 1920's when whole wards of kids were hit with a first dose that removed the symptoms in minutes. I can't imagine being in that room when all that despair and anguish turned into hope and relief.