Am I a Gemini ascendant or Cancer ascendant?

That is the problem with internet websites.
MOST of the astrological programs that calculate free charts have flaws in them. Often they calculate charts correctly, but sometimes they make errors.

Out of ALL the websites that I have checked out, only 2 are reliably accurate:
astro.com
alabe.com

The other problem is that you Ascendant is 0:55 Cancer. That means that even just a math error of 4 minutes clock time (earlier) would give you a Gemini Ascendant.
So any site that has even a slight calculation glitch could easily give you a different Ascendant.

I use a professional astrological software program (the kind you buy and install on your computer). I use Win*Star. The other 2 major programs used in North America are Solar Fire and Sirius.
Note that alabe.com site is posted BY Solar Fire makers, so it`s accuracy is good.
Astrologers base everything ON the chart, so we are real sticklers for accuracy. The reading is only as good as the chart is accurate, and we do not make guesses .. we read the chart AS it is.

So use alabe or astro for your websites dear.
And yes, you do have Cancer Rising.

NOTE:
The difference between an Ascendant of 0:50 Cancer and 0:55 Cancer is a difference of 20 seconds of clock time on your birth time. So negligible as to be irrelevant. It is common to find variations that small in the calculation of birth charts between the major professional programs.

In western astrology, tropical, according to Astrodienst and Astrolabe you are a Cancer rising at 0 degrees and 50 minutes and so I'd go with that unless you prefer Vedic astrology.
Your 2nd house also starts in Cancer, this is what may be confusing you if you're looking at a site that tables the houses in their signs. Opposite, your 7th and 8th houses are both in Capricorn; these are known as duplicated signs and are stronger, or have more influence over you, because they cover more areas of life.
Because of this, you have two signs that are intercepted, they have no house cusps in them; your Gemini and Sagittarius are both intercepted.

You are 0 Degrees Cancer Rising

Use astro.com for most accurate chart

gemini

you are Gemini rising dear

A perfect example of the absolute contradictory nonsense of astrology. One type tells you that you are this, another that, I'm not surprised by the fact that you are confused by it all. Neither is wrong or right, how does THAT work. Even MORE confusion! Suggestion: if you feel you have to take a look at astrology, try to view it as objectively as you possibly can. First rule: NEVER give anyone any money. Not for books (use a local library if you feel you must), pictures, 'readings', 'charts', access to websites, jewellery, posters, t-shirts, meetings, conventions or anything of the like. Second rule: put as much energy into reading why astrology DOESN'T work as you would into reading why it does (the objective part). This may initially appear contradictory, but it will equip you with the ability to make your own judgement as to the validity of claims made either way - afford you a less blinkered, more balanced view. Finally, be in total control of your own mind. You ARE allowed to disagree with anything. Challenge things.