Safety and Efficacy of PTH-IA

* INCLUSION CRITERIA: In order to be eligible to participate in this study, an individual must meet all of the following criteria: 1. Willingness of participant and/or guardian to sign a written informed consent form, which must be obtained prior to initiation of study procedures. 2. Period 1: Adults \>=18 years of age Period 2: Adults and children 3-17 years of age 3. Minimum body weight of 35 kg for participation in Period 1 and 18 kg for participation in Period 2. 4. Have an activating germline mutation of PTHIR (H223R, I458K, I458R, T410P, or T410R) 5. Female participants of reproductive potential must agree to use one form of highly effective contraception. Highly effective contraception includes: Total abstinence (when this is in line with the preferred and usual lifestyle of the participant). Periodic abstinence (e.g. calendar, ovulation, symptothermal, post- ovulation methods) and withdrawal are not acceptable methods of contraception. Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment. Male sterilization (at least 6 months prior to screening). For female participants in the study, the vasectomized male partner should be the sole partner for that participant for the study duration. Use of oral, injected, or implanted hormonal methods of contraception or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%), for example hormonal vaginal ring or transdermal hormone contraception Placement of an intrauterine device (IUD) or intrauterine system (IUS) Barrier methods of contraception used correctly by the male partner: condom or occlusive cap (diaphragm or cervical/ vault caps) with spermicidal foam/gel/film/cream/vaginal suppository. 6. For males of reproductive potential: use of condoms or other methods described above to ensure effective contraception with partner. 7. Stated willingness to comply with all study procedures and availability for the duration of the study, including the ability and willingness to travel to the NIH Clinical Center. EXCLUSION CRITERIA: An individual who meets any of the following criteria will be excluded from participation in this study: 1. Pregnancy or lactation 2. 25-hydroxyvitamin D \<=20 ng/mL. Patients will be eligible for rescreening after a repletion period lasting up to 6 months. 3. Clinically significant renal disease with estimated glomerular filtration rate (eGFR) \<=45 mL/ min/1.73 m2. 4. Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) \>2 times the upper limit of normal. If transaminitis is present, patients will be eligible for rescreening for a period of up to 6 months. 5. Hgb \<12 gm/dL for women and girls \>=16 years, \<=13 gm/dL for men and boys \>=16 years, and \<=11.5 gm/dL in children \<=15 years. If reduced hemoglobin levels are related to iron, B12, or folate deficiency, patients will be eligible for rescreening after a repletion period lasting up to 6 months. 6. Hypersensitivity or intolerance to any active substance or excipient of PTH-IA 7. History of surgical removal of all parathyroid glands. 8. Treatment with bisphosphonate use within 6 months of screening 9. Treatment with denosumab within 3 months of screening 10. Treatment with thiazides within 4 weeks of screening 11. Any other significant medical conditions that, in the opinion of the study team, may present a concern for participant safety or difficulty with data interpretation.