The goal of this clinical trial is to learn about the effect of the study drug (ZT-01) on low blood sugar (hypoglycemia) in adults with type 1 diabetes (T1D) who have been having low blood sugars (hypos) at night. ZT-01 increases the amount of a hormone called glucagon during low blood sugar, and this may help prevent the occurrence of hypos. The main questions this trial aims to answer are whether ZT-01 lowers the number of hypos happening at night, and what its effects are on blood sugar levels. The safety of ZT-01 will also be measured. Participants will be asked to wear a study-provided continuous glucose monitor (CGM) during two 4-week periods when they will self-inject the study drug before bed. They will get ZT-01 at one of three dose levels during one period, and placebo (which looks like the study drug but doesn't contain the active ingredient) during the other. Neither the participant nor the study site will know what they are receiving during each treatment period or see data from the CGM. The participant will continue to use their usual methods of measuring blood sugar (including their personal CGM) and giving insulin during the study. The participant will be asked to complete a short diary each evening, and will be asked to upload the CGM data to a study phone every day. If a participant uses their own CGM and is willing to share information on how often they have low blood sugar with the study site at the first visit to see if they meet study entry requirements, they will have 6 study visits, 2 study phone calls, and be in the study for about 16 weeks. If they don't use CGM or don't want to share their information, then they will be asked to wear a study CGM for an extra 4 weeks to find out how many low blood sugars they have, and will have an extra visit. Study participants will be asked to give blood and urine for testing to see whether they meet the requirements to enter the study, and at the start and end of each treatment period to see if the study treatment has any effects. They will also have their blood pressure and temperature taken at each study visit, and have an ECG at 4 visits to measure the electrical activity of their heart. Some participants will be asked to also take part in a sub-study where their blood level of ZT-01 and glucagon is measured, after the first and last dose. They will be asked to stay at the study site overnight for each set of measurements (4 in total).