As stated by user Stinkerbellkity, you cannot claim someone as a dependent who is incarcerated. There are a number of requirements that would not be met.
Since you stated your relationship is 'significant other', that would mean that she would have to qualify as your dependent under the qualifying relative requirements. One of these requirements is that they must have lived with you all year. If she is incarcerated, that requirement has not been met. The other main requirement is that you would have had to provide over half of her financial support for the basic life necessities such as food, lodging, medical care, etc. Those things are not being provided by you.
To learn more, see the following TurboTax article: Who can I claim as my dependent?
@grenade15