The information in this preliminary prospectus supplement and the accompanying prospectus is not complete and may be changed.This preliminary prospectus supplement and the accompanying prospectus are not an offer to sell these securities and we are notsoliciting an offer to buy these securities in any jurisdiction where the offer or sale is not permitted. Filed Pursuant to Rule 424(b)(5)Registration No. 333-292646 PRELIMINARY PROSPECTUS SUPPLEMENT(To Prospectus dated January 9, 2026) Celcuity Inc. $400,000,000 % Convertible Senior Notes due 2032 We are offering $400,000,000 aggregate principal amount of our% convertible senior notes due 2032 (the “notes”). MATURITY; INTEREST We will pay interest on the notes at an annual rate of%, payable semi-annually in arrears on February 1 and August 1 of each year,beginning on February 1, 2027. The notes will mature on August 1, 2032, unless earlier converted, redeemed or repurchased by us. CONVERSION Noteholders may convert their notes at their option only in the following circumstances: (1) during any calendar quarter (and only duringsuch calendar quarter) commencing after the calendar quarter ending on September 30, 2026, if the last reported sale price per share of ourcommon stock, $0.001 par value per share (the “common stock”), exceeds 130% of the conversion price for each of at least 20 trading days,whether or not consecutive, during the 30 consecutive trading days ending on, and including, the last trading day of the immediately precedingcalendar quarter; (2) during the five consecutive business days immediately after any 10 consecutive trading day period (such 10 consecutivetrading day period, the “measurement period”) in which the trading price per $1,000 principal amount of notes for each trading day of themeasurement period was less than 98% of the product of the last reported sale price per share of our common stock on such trading day and theconversion rate on such trading day; (3) upon the occurrence of certain corporate events or distributions on our common stock, as described inthis prospectus supplement; (4) if we call such notes for redemption; and (5) at any time from, and including, May 1, 2032 until the close ofbusiness on the scheduled trading day immediately before the maturity date. We will settle conversions by paying or delivering, as applicable,cash, shares of our common stock or a combination of cash and shares of our common stock, at our election, based on the applicable conversionrate. The initial conversion rate isshares of common stock per $1,000 principal amount of notes, which represents an initial conversionprice of approximately $per share, and is subject to adjustment as described in this prospectus supplement. If a “make-whole fundamentalchange” (as defined in this prospectus supplement) occurs, then we will in certain circumstances increase the conversion rate for a specifiedperiod of time. REDEMPTION AND REPURCHASE We may not redeem the notes at our option at any time before August 6, 2029. The notes will be redeemable, in whole or in part (subject tocertain limitations described in this prospectus supplement), at our option at any time, and from time to time, on a redemption date on or afterAugust 6, 2029 and on or before the 31st scheduled trading day immediately before the maturity date, at a cash redemption price equal to theprincipal amount of the notes to be redeemed, plus accrued and unpaid interest, if any, to, but excluding, the redemption date, but only if thelast reported sale price per share of our common stock exceeds 130% of the conversion price on (1) each of at least 20 trading days, whether ornot consecutive, during the 30 consecutive trading days ending on, and including, the trading day immediately before the date we send therelated redemption notice; and (2) the trading day immediately before the date we send such notice. In addition, calling any note for redemptionwill constitute a make-whole fundamental change with respect to that note, in which case the conversion rate applicable to the conversion ofthat note will be increased in certain circumstances if it is converted after it is called for redemption. If a “fundamental change” (as defined in this prospectus supplement) occurs, then, except as described in this prospectus supplement,noteholders may require us to repurchase their notes at a cash repurchase price equal to the principal amount of the notes to be repurchased,plus accrued and unpaid interest, if any, to, but excluding, the fundamental change repurchase date. RANKING The notes will be our general, unsecured, senior obligations and will be senior in right of payment to our future indebtedness that isexpressly subordinated in right of payment to the notes, equal in right of payment with our existing and future indebtedness that is not expresslysubordinated to the notes, including our 2.750% Convertible Senior Notes due 2031 (the “2031 Notes”), and effectively subordinated to ourex